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

## 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

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]

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

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

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 ...

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 + 13 × 15 + ... 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Find 122 + 132 + 142 + 152 + ... 202

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

## Chapter 2: Sequences and Series

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4Exercise 2.5Exercise 2.6Miscellaneous Exercise 2

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

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