Maharashtra State BoardHSC Science (General) 11th
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Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board chapter 2 - Sequences and Series [Latest edition]

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Chapters

Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board - Shaalaa.com

Chapter 2: Sequences and Series

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4Exercise 2.5Exercise 2.6Miscellaneous Exercise 2
Exercise 2.1 [Pages 27 - 28]

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board Chapter 2 Sequences and Series Exercise 2.1 [Pages 27 - 28]

Exercise 2.1 | Q 1. (i) | Page 27

Check whether the following sequence is G.P. If so, write tn.

2, 6, 18, 54, …

Exercise 2.1 | Q 1. (ii) | Page 27

Check whether the following sequence is G.P. If so, write tn.

1, –5, 25, –125 …

Exercise 2.1 | Q 1. (iii) | Page 27

Check whether the following sequence is G.P. If so, write tn.

`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5))`, ...

Exercise 2.1 | Q 1. (iv) | Page 27

Check whether the following sequence is G.P. If so, write tn.

3, 4, 5, 6, …

Exercise 2.1 | Q 1. (v) | Page 27

Check whether the following sequence is G.P. If so, write tn.

7, 14, 21, 28, …

Exercise 2.1 | Q 2. (i) | Page 27

For the G.P. if r = `1/3`, a = 9 find t7

Exercise 2.1 | Q 2. (ii) | Page 27

For the G.P. if a = `7/243`, r = 3 find t6

Exercise 2.1 | Q 2. (iii) | Page 27

For the G.P. if r = − 3 and t6 = 1701, find a.

Exercise 2.1 | Q 2. (iv) | Page 27

For the G.P. if a = `2/3`, t6 = 162, find r.

Exercise 2.1 | Q 3 | Page 27

Which term of the G.P. 5, 25, 125, 625, … is 510?

Exercise 2.1 | Q 4 | Page 27

For what values of x, the terms `4/3`, x, `4/27` are in G.P.?

Exercise 2.1 | Q 5 | Page 27

If for a sequence, tn = `(5^("n"-3))/(2^("n"-3))`, show that the sequence is a G.P. Find its first term and the common ratio

Exercise 2.1 | Q 6 | Page 27

Find three numbers in G.P. such that their sum is 21 and sum of their squares is 189.

Exercise 2.1 | Q 7 | Page 27

Find four numbers in G.P. such that sum of the middle two numbers is `10/3` and their product is 1

Exercise 2.1 | Q 8 | Page 27

Find five numbers in G.P. such that their product is 1024 and fifth term is square of the third term.

Exercise 2.1 | Q 9 | Page 27

The fifth term of a G.P. is x, eighth term of a G.P. is y and eleventh term of a G.P. is z verify whether y2 = xz

Exercise 2.1 | Q 10 | Page 27

If p, q, r, s are in G.P. show that p + q, q + r, r + s are also in G.P.

Exercise 2.1 | Q 11 | Page 27

The number of bacteria in a culture doubles every hour. If there were 50 bacteria originally in the culture, how many bacteria will be there at the end of 5thhour?

Exercise 2.1 | Q 12 | Page 27

A ball is dropped from a height of 80 ft. The ball is such that it rebounds `(3/4)^"th"` of the height it has fallen. How high does the ball rebound on 6th bounce? How high does the ball rebound on nth bounce?

Exercise 2.1 | Q 13. (i) | Page 28

The numbers 3, x, and x + 6 form are in G.P. Find x

Exercise 2.1 | Q 13. (ii) | Page 28

The numbers 3, x, and x + 6 form are in G.P. Find 20th term

Exercise 2.1 | Q 13. (iii) | Page 28

The numbers 3, x, and x + 6 form are in G.P. Find nth term

Exercise 2.1 | Q 14. (i) | Page 28

Mosquitoes are growing at a rate of 10% a year. If there were 200 mosquitoes in the beginning. Write down the number of mosquitoes after 3 years.

Exercise 2.1 | Q 14. (ii) | Page 28

Mosquitoes are growing at a rate of 10% a year. If there were 200 mosquitoes in the beginning. Write down the number of mosquitoes after 10 years.

Exercise 2.1 | Q 14. (iii) | Page 28

Mosquitoes are growing at a rate of 10% a year. If there were 200 mosquitoes in the beginning. Write down the number of mosquitoes after n years.

Exercise 2.1 | Q 15. (i) | Page 28

The numbers x − 6, 2x and x2 are in G.P. Find x

Exercise 2.1 | Q 15. (ii) | Page 28

The numbers x − 6, 2x and x2 are in G.P. Find 1st term

Exercise 2.1 | Q 15. (iii) | Page 28

The numbers x − 6, 2x and x2 are in G.P. Find nth term

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Exercise 2.2 [Pages 31 - 32]

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board Chapter 2 Sequences and Series Exercise 2.2 [Pages 31 - 32]

Exercise 2.2 | Q 1. (i) | Page 31

For the following G.P.s, find Sn

3, 6, 12, 24, ...

Exercise 2.2 | Q 1. (ii) | Page 31

For the following G.P.s, find Sn

p, q, `"q"^2/"p", "q"^3/"p",` ...

Exercise 2.2 | Q 1. (iii) | Page 31

For the following G.P.s, find Sn

0.7, 0.07, 0.007, .....

Exercise 2.2 | Q 1. (iv) | Page 31

For the following G.P.s, find Sn

`sqrt(5)`, −5, `5sqrt(5)`, −25 ...

Exercise 2.2 | Q 2. (i) | Page 31

For a G.P. a = 2, r = `-2/3`, find S6

Exercise 2.2 | Q 2. (ii) | Page 31

For a G.P. if S5 = 1023 , r = 4, Find a

Exercise 2.2 | Q 3. (i) | Page 31

For a G.P. if a = 2, r = 3, Sn = 242 find n

Exercise 2.2 | Q 3. (ii) | Page 31

For a G.P. sum of first 3 terms is 125 and sum of next 3 terms is 27, find the value of r

Exercise 2.2 | Q 4. (i) | Page 31

For a G.P. If t3 = 20 , t6 = 160 , find S7

Exercise 2.2 | Q 4. (ii) | Page 31

For a G.P. If t4 = 16, t9 = 512, find S10

Exercise 2.2 | Q 5. (i) | Page 31

Find the sum to n terms 3 + 33 + 333 + 3333 + …

Exercise 2.2 | Q 5. (ii) | Page 31

Find the sum to n terms 8 + 88 + 888 + 8888 + ...

Exercise 2.2 | Q 6. (i) | Page 31

Find the sum to n terms 0.4 + 0.44 + 0.444 + ...

Exercise 2.2 | Q 6. (ii) | Page 31

Find the sum to n terms 0.7 + 0.77 + 0.777 + ...

Exercise 2.2 | Q 7. (i) | Page 31

Find the sum to n terms of the sequence.

0.5, 0.05, 0.005, ...

Exercise 2.2 | Q 7. (ii) | Page 31

Find the sum to n terms of the sequence.

0.2, 0.02, 0.002, ...

Exercise 2.2 | Q 8 | Page 32

For a sequence, if Sn = 2(3n –1), find the nth term, hence show that the sequence is a G.P.

Exercise 2.2 | Q 9 | Page 32

If S, P, R are the sum, product, and sum of the reciprocals of n terms of a G.P. respectively, then verify that `["S"/"R"]^"n"` = P

Exercise 2.2 | Q 10 | Page 32

If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn (S3n – S2n) = (S2n – Sn)2.

Exercise 2.2 | Q 11. (i) | Page 32

Find: `sum_("r" = 1)^10(3 xx 2^"r")`

Exercise 2.2 | Q 11. (ii) | Page 32

Find: `sum_("r" = 1)^10 5 xx 3^"r"`

Exercise 2.2 | Q 12 | Page 32

The value of a house appreciates 5% per year. How much is the house worth after 6 years if its current worth is ₹ 15 Lac. [Given: (1.05)5 = 1.28, (1.05)6 = 1.34]

Exercise 2.2 | Q 13 | Page 32

If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum, how long does it take to double the money by compound interest? [(1.08)5 = 1.47]

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Exercise 2.3 [Pages 33 - 34]

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board Chapter 2 Sequences and Series Exercise 2.3 [Pages 33 - 34]

Exercise 2.3 | Q 1. (i) | Page 33

Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

`1/2, 1/4, 1/8, 1/16,...`

Exercise 2.3 | Q 1. (ii) | Page 33

Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

`2, 4/3, 8/9, 16/27, ...`

Exercise 2.3 | Q 1. (iii) | Page 33

Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

`-3, 1, (-1)/3, 1/9, ...`

Exercise 2.3 | Q 1. (iv) | Page 33

Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

`1/5, (-2)/5, 4/5, (-8)/5, 16/5, ...`

Exercise 2.3 | Q 1. (v) | Page 33

Determine whether the sum to infinity of the following G.P.s exist, if exists find them:

9, 8.1, 7.29, ...

Exercise 2.3 | Q 2. (i) | Page 33

Express the following recurring decimal as a rational number:

`0.bar(7)`

Exercise 2.3 | Q 2. (ii) | Page 33

Express the following recurring decimal as a rational number:

`2.bar(4)`

Exercise 2.3 | Q 2. (iii) | Page 33

Express the following recurring decimal as a rational number:

`2.3bar(5)`

Exercise 2.3 | Q 2. (iv) | Page 33

Express the following recurring decimal as a rational number:

`51.0bar(2)`

Exercise 2.3 | Q 3 | Page 33

If the common ratio of a G.P. is `2/3` and sum to infinity is 12. Find the first term

Exercise 2.3 | Q 4 | Page 33

If the first term of the G.P. is 16 and its sum to infinity is `96/17` find the common ratio

Exercise 2.3 | Q 5 | Page 34

The sum of an infinite G.P. is 5 and the sum of the squares of these terms is 15 find the G.P.

Exercise 2.3 | Q 6. (i) | Page 34

Find : `sum_("r" = 1)^oo 4(0.5)^"r"`

Exercise 2.3 | Q 6. (ii) | Page 34

Find : `sum_("r" = 1)^oo (-1/3)^"r"`

Exercise 2.3 | Q 6. (iii) | Page 34

Find : `sum_("r" = 0)^oo (-8)(-1/2)^"n"`

Exercise 2.3 | Q 6. (iv) | Page 34

Find : `sum_("n" = 1)^oo 0.4^"n"`

Exercise 2.3 | Q 7. (i) | Page 34

The midpoints of the sides of a square of side 1 are joined to form a new square. This procedure is repeated indefinitely. Find the sum of the areas of all the squares

Exercise 2.3 | Q 7. (ii) | Page 34

The midpoints of the sides of a square of side 1 are joined to form a new square. This procedure is repeated indefinitely. Find the sum of the perimeters of all the squares

Exercise 2.3 | Q 8 | Page 34

A ball is dropped from a height of 10m. It bounces to a height of 6m, then 3.6m and so on. Find the total distance travelled by the ball

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Exercise 2.4 [Page 37]

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board Chapter 2 Sequences and Series Exercise 2.4 [Page 37]

Exercise 2.4 | Q 1. (i) | Page 37

Verify whether the following sequence is H.P.

`1/3, 1/5, 1/7, 1/9, ...`

Exercise 2.4 | Q 1. (ii) | Page 37

Verify whether the following sequence is H.P.

`1/3, 1/6, 1/12, 1/24, ...`

Exercise 2.4 | Q 1. (iii) | Page 37

Verify whether the following sequence is H.P.

`5, 10/17, 10/32, 10/47, ...`

Exercise 2.4 | Q 2. (i) | Page 37

Find the nth term and hence find the 8th term of the following H.P.s :

`1/2, 1/5, 1/8, 1/11, ...`

Exercise 2.4 | Q 2. (ii) | Page 37

Find the nth term and hence find the 8th term of the following H.P.s :

`1/4, 1/6, 1/8, 1/10, ...`

Exercise 2.4 | Q 2. (iii) | Page 37

Find the nth term and hence find the 8th term of the following H.P.s :

`1/5, 1/10, 1/15, 1/20, ...`

Exercise 2.4 | Q 3 | Page 37

Find A.M. of two positive numbers whose G.M. and H.M. are 4 and `16/5` respectively.

Exercise 2.4 | Q 4 | Page 37

Find H.M. of two positive numbers A.M. and G.M. are `15/2` and 6

Exercise 2.4 | Q 5 | Page 37

Find GM of two positive numbers whose A.M. and H.M. are 75 and 48

Exercise 2.4 | Q 6 | Page 37

Insert two numbers between `1/4` and `1/3` so that the resulting sequence is a H.P.

Exercise 2.4 | Q 7 | Page 37

Insert two numbers between 1 and −27 so that the resulting sequence is a G.P.

Exercise 2.4 | Q 8 | Page 37

If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by `18/5`, find the numbers.

Exercise 2.4 | Q 9 | Page 37

Find two numbers whose A.M. exceeds their G.M. by `1/2` and their H.M. by `25/26`

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Exercise 2.5 [Page 38]

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board Chapter 2 Sequences and Series Exercise 2.5 [Page 38]

Exercise 2.5 | Q 1. (i) | Page 38

Find Sn of the following arithmetico - geometric sequence: 

2, 4x, 6x2, 8x3, 10x4, …

Exercise 2.5 | Q 1. (ii) | Page 38

Find Sn of the following arithmetico - geometric sequence: 

1, 4x, 7x2, 10x3, 13x4, …

Exercise 2.5 | Q 1. (iii) | Page 38

Find Sn of the following arithmetico - geometric sequence:

1, 2 × 3, 3 × 9, 4 × 27, 5 × 81, …

Exercise 2.5 | Q 1. (iv) | Page 38

Find Sn of the following arithmetico - geometric sequence:

3, 12, 36, 96, 240, …

Exercise 2.5 | Q 2. (i) | Page 38

Find the sum to infinity of the following arithmetico - geometric sequence:

`1, 2/4, 3/16, 4/64, ...`

Exercise 2.5 | Q 2. (ii) | Page 38

Find the sum to infinity of the following arithmetico - geometric sequence:

`3, 6/5, 9/25, 12/125, 15/625, ...`

Exercise 2.5 | Q 2. (iii) | Page 38

Find the sum to infinity of the following arithmetico - geometric sequence:

`1, -4/3, 7/9, -10/27 ...`

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Exercise 2.6 [Page 40]

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board Chapter 2 Sequences and Series Exercise 2.6 [Page 40]

Exercise 2.6 | Q 1 | Page 40

Find the sum `sum_("r" = 1)^"n" ("r" + 1)(2"r" - 1)`

Exercise 2.6 | Q 2 | Page 40

Find `sum_("r" = 1)^"n"(3"r"^2 - 2"r" + 1)`

Exercise 2.6 | Q 3 | Page 40

Find `sum_("r" = 1)^"n"((1 + 2 + 3  .... +  "r")/"r")`

Exercise 2.6 | Q 4 | Page 40

Find `sum_("r" = 1)^"n" [(1^3 + 2^3 + .... +  "r"^3)/("r"("r" + 1))]`

Exercise 2.6 | Q 5 | Page 40

Find the sum 5 × 7 + 9 × 11 + 11 × 3 + ... upto n terms

Exercise 2.6 | Q 6 | Page 40

Find the sum 22 + 42 + 62 + 82 + ... upto n terms

Exercise 2.6 | Q 7 | Page 40

Find (702 – 692) + (682 – 672) + (662 – 652) + ... + (22 – 12)

Exercise 2.6 | Q 8 | Page 40

Find the sum 1 × 3 × 5 + 3 × 5 × 7 + 5 × 7 × 9 + ... + (2n – 1) (2n + 1) (2n + 3)

Exercise 2.6 | Q 9 | Page 40

If `(1 xx 2 + 2 xx 3 + 3 xx 4 + 4 xx 5 + ...  "upto n terms")/(1 + 2 + 3 + 4 + ...  "upto n terms") = 100/3,` find n

Exercise 2.6 | Q 10 | Page 40

If S1, S2 and S3 are the sums of first n natural numbers, their squares and their cubes respectively then show that - 9S22 = S3 (1 + 8 S1

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Miscellaneous Exercise 2 [Pages 40 - 41]

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board Chapter 2 Sequences and Series Miscellaneous Exercise 2 [Pages 40 - 41]

Miscellaneous Exercise 2 | Q I. (1) | Page 40

Select the correct answer from the given alternative.

The common ratio for the G.P. 0.12, 0.24, 0.48, is –

  • 0.12

  • 0.2

  • 0.02

  • 2

Miscellaneous Exercise 2 | Q I. (2) | Page 40

Select the correct answer from the given alternative.

The tenth term of the geometric sequence `1/4, (-1)/2, 1, -2,` ... is –

  • 1024

  • `1/1024`

  • – 128

  • `(-1)/28`

Miscellaneous Exercise 2 | Q I. (3) | Page 41

Select the correct answer from the given alternative.

If for a G.P. `"t"_6/"t"_3 = 1458/54` then r = ?

  • 3

  • 2

  • 1

  • – 1

Miscellaneous Exercise 2 | Q I. (4) | Page 41

Select the correct answer from the given alternative.

Which term of the geometric progression 1, 2, 4, 8, ... is 2048

  • 10th 

  • 11th 

  • 12th 

  • 13th 

Miscellaneous Exercise 2 | Q I. (5) | Page 41

Select the correct answer from the given alternative.

If common ratio of the G.P is 5, 5th term is 1875, the first term is -

  • 3

  • 5

  • 15

  • – 5

Miscellaneous Exercise 2 | Q I. (6) | Page 41

Select the correct answer from the given alternative.

The sum of 3 terms of a G.P. is `21/4` and their product is 1 then the common ratio is –

  • 1

  • 2

  • 4

  • 8

Miscellaneous Exercise 2 | Q I. (7) | Page 41

Select the correct answer from the given alternative.

Sum to infinity of a G.P. 5, `-5/2, 5/4, -5/8, 5/16,...` is –

  • 5

  • `-1/2`

  • `10/3`

  • `3/10`

Miscellaneous Exercise 2 | Q I. (8) | Page 41

Select the correct answer from the given alternative.

The tenth term of H.P. `2/9, 1/7, 2/19, 1/12, ...` is –

  • `1/27`

  • `9/2`

  • `5/2`

  • 27

Miscellaneous Exercise 2 | Q I. (9) | Page 41

Select the correct answer from the given alternative.

Which of the following is not true, where A, G, H are the AM, GM, HM of a and b respectively. (a, b > 0)

  • A = `("a" + "b")/2`

  • G = `sqrt("ab")`

  • H = `(2"ab")/("a" + "b")`

  • A = GH

Miscellaneous Exercise 2 | Q I. (10) | Page 41

Select the correct answer from the given alternative.

The G.M.of two numbers exceeds their H.M. by `6/5`, the A.M. exceeds G.M. by `3/2` the two numbers are ...

  • `6, 15/2`

  • 15, 25

  • 3, 12

  • `6/5, 3/2`

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Miscellaneous Exercise 2 [Pages 41 - 42]

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board Chapter 2 Sequences and Series Miscellaneous Exercise 2 [Pages 41 - 42]

Miscellaneous Exercise 2 | Q II. (1) | Page 41

Answer the following:

In a G.P., the fourth term is 48 and the eighth term is 768. Find the tenth term

Miscellaneous Exercise 2 | Q II. (2) | Page 41

Answer the following:

Find the sum of the first 5 terms of the G.P. whose first term is 1 and common ratio is `2/3`

Miscellaneous Exercise 2 | Q II. (3) | Page 41

Answer the following:

For a G.P. a = `4/3` and t7 = `243/1024`, find the value of r

Miscellaneous Exercise 2 | Q II. (4) | Page 41

Answer the following:

For a sequence , if tn = `(5^("n" - 2))/(7^("n" - 3))`, verify whether the sequence is a G.P. If it is a G.P., find its first term and the common ratio.

Miscellaneous Exercise 2 | Q II. (5) | Page 41

Answer the following:

Find three numbers in G.P. such that their sum is 35 and their product is 1000

Miscellaneous Exercise 2 | Q II. (6) | Page 41

Answer the following:

Find five numbers in G.P. such that their product is 243 and sum of second and fourth number is 10.

Miscellaneous Exercise 2 | Q II. (7) | Page 41

Answer the following:

For a sequence Sn = 4(7n – 1) verify that the sequence is a G.P.

Miscellaneous Exercise 2 | Q II. (8) | Page 41

Answer the following:

Find 2 + 22 + 222 + 2222 + ... upto n terms

Miscellaneous Exercise 2 | Q II. (9) | Page 41

Answer the following:

Find the nth term of the sequence 0.6, 0.66, 0.666, 0.6666, ...

Miscellaneous Exercise 2 | Q II. (10) | Page 41

Answer the following:

Find `sum_("r" = 1)^"n" (5"r"^2 + 4"r" - 3)`

Miscellaneous Exercise 2 | Q II. (11) | Page 41

Answer the following:

Find `sum_("r" = 1)^"n" "r"("r" - 3)("r" - 2)`

Miscellaneous Exercise 2 | Q II. (12) | Page 41

Answer the following:

Find `sum_("r" = 1)^"n" ((1^2 + 2^2 + 3^2 + ... + "r"^2)/(2"r" + 1))`

Miscellaneous Exercise 2 | Q II. (13) | Page 41

Answer the following:

Find `sum_("r" = 1)^"n" ((1^3 + 2^3 + 3^3 + ... "r"^3)/("r" + 1)^2)`

Miscellaneous Exercise 2 | Q II. (14) | Page 41

Answer the following:

Find 2 × 6 + 4 × 9 + 6 × 12 + ... upto n terms

Miscellaneous Exercise 2 | Q II. (15) | Page 41

Answer the following:

Find 2 × 5 × 8 + 4 × 7 × 10 + 6 × 9 × 12 + ... upto n terms

Miscellaneous Exercise 2 | Q II. (16) | Page 42

Answer the following:

Find `1^2/1 + (1^2 + 2^2)/2 + (1^2 + 2^2 + 3^2)/3 + ...` upto n terms

Miscellaneous Exercise 2 | Q II. (17) | Page 42

Answer the following:

Find 122 + 132 + 142 + 152 + ... 202 

Miscellaneous Exercise 2 | Q II. (18) | Page 42

Answer the following:

If `(1 + 2 + 3 + 4 + 5 + ...  "upto n terms")/(1 xx 2 + 2 xx3 + 3 xx 4 + 4 xx5 + ...  "upto n terms") = 3/22` Find the value of n 

Miscellaneous Exercise 2 | Q II. (19) | Page 42

Answer the following:

Find (502 – 492) + (482 – 472) + (462 – 452) + ... + (22 – 12)

Miscellaneous Exercise 2 | Q II. (20) | Page 42

Answer the following:

If  `(1 xx 3 + 2 xx 5 + 3 xx 7 + ...  "upto n terms")/(1^3 + 2^3 + 3^3 + ...  "upto n terms") = 5/9`, find the value of n

Miscellaneous Exercise 2 | Q II. (21) | Page 42

Answer the following:

For a G.P. if t2 = 7, t4 = 1575 find a

Miscellaneous Exercise 2 | Q II. (22) | Page 42

Answer the following:

If for a G.P. t3 = `1/3`, t6 = `1/81` find r

Miscellaneous Exercise 2 | Q II. (23) | Page 42

Answer the following:

Find `sum_("r" = 1)^"n" (2/3)^"r"`

Miscellaneous Exercise 2 | Q II. (24) | Page 42

Answer the following:

Find k so that k – 1, k, k + 2 are consecutive terms of a G.P.

Miscellaneous Exercise 2 | Q II. (25) | Page 42

Answer the following:

If for a G.P. first term is (27)2 and seventh term is (8)2, find S8 

Miscellaneous Exercise 2 | Q II. (26) | Page 42

Answer the following:

If pth, qth and rth terms of a G.P. are x, y, z respectively. Find the value of xq–r .yr–p .zp–q

Miscellaneous Exercise 2 | Q II. (27) | Page 42

Answer the following:

Which 2 terms are inserted between 5 and 40 so that the resulting sequence is G.P.

Miscellaneous Exercise 2 | Q II. (28) | Page 42

Answer the following:

If p, q, r are in G.P. and `"p"^(1/x) = "q"^(1/y) = "r"^(1/z)`, verify whether x, y, z are in A.P. or G.P. or neither.

Miscellaneous Exercise 2 | Q II. (29) | Page 42

Answer the following:

If a, b, c are in G.P. and ax2 + 2bx + c = 0 and px2 + 2qx + r = 0 have common roots then verify that pb2 – 2qba + ra2 = 0

Miscellaneous Exercise 2 | Q II. (30) | Page 42

Answer the following:

If p, q, r, s are in G.P., show that (p2 + q2 + r2) (q2 + r2 + s2) = (pq + qr + rs)2   

Miscellaneous Exercise 2 | Q II. (31) | Page 42

Answer the following:

If p, q, r, s are in G.P., show that (pn + qn), (qn + rn) , (rn + sn) are also in G.P.

Miscellaneous Exercise 2 | Q II. (32) | Page 42

Answer the following:

Find the coefficient of x6 in the expansion of e2x using series expansion

Miscellaneous Exercise 2 | Q II. (33) | Page 42

Answer the following:

Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`

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Chapter 2: Sequences and Series

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4Exercise 2.5Exercise 2.6Miscellaneous Exercise 2
Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board - Shaalaa.com

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board chapter 2 - Sequences and Series

Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board chapter 2 (Sequences and Series) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board chapter 2 Sequences and Series are Concept of Sequences, Arithmetic Progression (A.P.), Geometric Progression (G. P.), Harmonic Progression (H. P.), Arithmetico Geometric Series, Power Series.

Using Balbharati 11th solutions Sequences and Series exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 11th prefer Balbharati Textbook Solutions to score more in exam.

Get the free view of chapter 2 Sequences and Series 11th extra questions for Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board and can use Shaalaa.com to keep it handy for your exam preparation

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