Maharashtra State BoardHSC Commerce 11th
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Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 4 - Sequences and Series [Latest edition]

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Chapters

Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board - Shaalaa.com

Chapter 4: Sequences and Series

Exercise 4.1Exercise 4.2Exercise 4.3Exercise 4.4Exercise 4.5Miscellaneous Exercise 4
Exercise 4.1 [Pages 50 - 51]

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 4 Sequences and Series Exercise 4.1 [Pages 50 - 51]

Exercise 4.1 | Q 1. (i) | Page 50

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

2, 6, 18, 54, ...

Exercise 4.1 | Q 1. (ii) | Page 50

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

1, – 5, 25, – 125, ...

Exercise 4.1 | Q 1. (iii) | Page 50

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

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

Exercise 4.1 | Q 1. (iv) | Page 50

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

3, 4, 5, 6, ...

Exercise 4.1 | Q 1. (v) | Page 50

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

7, 14, 21, 28, ...

Exercise 4.1 | Q 2. (i) | Page 50

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

Exercise 4.1 | Q 2. (ii) | Page 50

For the G.P., if a = `7/243, "r" = 1/3`, find t3.

Exercise 4.1 | Q 2. (iii) | Page 50

For the G.P., if a = 7, r = – 3, find t6.

Exercise 4.1 | Q 2. (iv) | Page 50

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

Exercise 4.1 | Q 3 | Page 50

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

Exercise 4.1 | Q 4 | Page 50

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

Exercise 4.1 | Q 5 | Page 50

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

Exercise 4.1 | Q 6 | Page 51

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

Exercise 4.1 | Q 7 | Page 51

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

Exercise 4.1 | Q 8 | Page 51

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

Exercise 4.1 | Q 9 | Page 51

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

Exercise 4.1 | Q 10 | Page 51

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

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Exercise 4.2 [Pages 54 - 55]

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 4 Sequences and Series Exercise 4.2 [Pages 54 - 55]

Exercise 4.2 | Q 1. (i) | Page 54

For the following G.P.'s, find Sn: 3, 6, 12, 24, ...

Exercise 4.2 | Q 1. (ii) | Page 54

For the following G.P.'s, find Sn: p, q, `"q"^2/"p", "q"^3/"p"^2`, ...

Exercise 4.2 | Q 2. (i) | Page 54

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

Exercise 4.2 | Q 2. (ii) | Page 54

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

Exercise 4.2 | Q 3. (i) | Page 54

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

Exercise 4.2 | Q 3. (ii) | Page 54

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

Exercise 4.2 | Q 4. (i) | Page 55

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

Exercise 4.2 | Q 4. (ii) | Page 55

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

Exercise 4.2 | Q 5. (i) | Page 55

Find the sum to n terms: 3 + 33 + 333 + 3333 + ...

Exercise 4.2 | Q 5. (ii) | Page 55

Find the sum to n terms: 8 + 88 + 888 + 8888 + …

Exercise 4.2 | Q 6. (i) | Page 55

Find the sum to n term: 0.4 + 0.44 + 0.444 + …

Exercise 4.2 | Q 6. (ii) | Page 55

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

Exercise 4.2 | Q 7. (i) | Page 55

Find the nth terms of the sequences: 0.5, 0.55, 0.555, …

Exercise 4.2 | Q 7. (ii) | Page 55

Find the nth terms of the sequences:  0.2, 0.22, 0.222, …

Exercise 4.2 | Q 8 | Page 55

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

Exercise 4.2 | Q 9 | Page 55

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"^2`.

Exercise 4.2 | Q 10 | Page 55

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.

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Exercise 4.3 [Pages 56 - 57]

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 4 Sequences and Series Exercise 4.3 [Pages 56 - 57]

Exercise 4.3 | Q 1. (i) | Page 56

Determine whether the sum to infinity of the following G.P’.s exist. If exists, find it:

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

Exercise 4.3 | Q 1. (ii) | Page 56

Determine whether the sum to infinity of the following G.P’.s exist. If exists, find it:

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

Exercise 4.3 | Q 1. (iii) | Page 56

Determine whether the sum to infinity of the following G.P’.s exist. If exists, find it:

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

Exercise 4.3 | Q 1. (iv) | Page 57

Determine whether the sum to infinity of the following G.P’.s exist. If exists, find it:

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

Exercise 4.3 | Q 2. (i) | Page 57

Express the following recurring decimal as a rational number:

`0.bar32`

Exercise 4.3 | Q 2. (ii) | Page 57

Express the following recurring decimals as a rational number:

`3.dot5`

Exercise 4.3 | Q 2. (iii) | Page 57

Express the following recurring decimals as a rational number:

`4.bar18`

Exercise 4.3 | Q 2. (iv) | Page 57

Express the following recurring decimals as a rational number:

`0.3bar45`

Exercise 4.3 | Q 2. (v) | Page 57

Express the following recurring decimals as a rational number: `3.4bar56`

Exercise 4.3 | Q 3 | Page 57

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

Exercise 4.3 | Q 4 | Page 57

If the first term of a G.P. is 16 and sum of its terms to infinity is `176/5`, find the common ratio.

Exercise 4.3 | Q 5 | Page 57

The sum of the terms of an infinite G.P. is 5 and the sum of the squares of those terms is 15. Find the G.P.

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Exercise 4.4 [Pages 60 - 61]

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 4 Sequences and Series Exercise 4.4 [Pages 60 - 61]

Exercise 4.4 | Q 1. (i) | Page 60

Verify whether the following sequence is H.P.:

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

Exercise 4.4 | Q 1. (ii) | Page 60

Verify whether the following sequence is H.P.:

`1/3, 1/6, 1/9, 1/12`, ... 

Exercise 4.4 | Q 1. (iii) | Page 60

Verify whether the following sequence is H.P.:

`1/7, 1/9, 1/11, 1/13, 1/15`, ...

Exercise 4.4 | Q 2. (i) | Page 60

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 4.4 | Q 2. (ii) | Page 60

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 4.4 | Q 2. (iii) | Page 60

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 4.4 | Q 3 | Page 60

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

Exercise 4.4 | Q 4 | Page 60

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

Exercise 4.4 | Q 5 | Page 60

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

Exercise 4.4 | Q 6 | Page 60

Insert two numbers between `1/7 and 1/13` so that the resulting sequence is a H.P.

Exercise 4.4 | Q 7 | Page 60

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

Exercise 4.4 | Q 8 | Page 60

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

Exercise 4.4 | Q 9 | Page 61

Find two numbers whose A.M. exceeds G.M. by 7 and their H.M. by `63/5`.

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Exercise 4.5 [Page 63]

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 4 Sequences and Series Exercise 4.5 [Page 63]

Exercise 4.5 | Q 1 | Page 63

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

Exercise 4.5 | Q 2 | Page 63

Find \[\displaystyle\sum_{r=1}^{n} (3r^2 - 2r + 1)\].

Exercise 4.5 | Q 3 | Page 63

Find \[\displaystyle\sum_{r=1}^{n}\frac{1 + 2 + 3 + ...+ r}{r}\]

Exercise 4.5 | Q 4 | Page 63

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

Exercise 4.5 | Q 5 | Page 63

Find the sum 5 x 7 + 7 x 9 + 9 x 11 x 13 + ... upto n terms.

Exercise 4.5 | Q 6 | Page 63

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

Exercise 4.5 | Q 7 | Page 63

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

Exercise 4.5 | Q 8 | Page 63

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

Exercise 4.5 | Q 9 | Page 63

Find n, 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`.

Exercise 4.5 | Q 10 | Page 63

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 + 8S1).

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Miscellaneous Exercise 4 [Pages 63 - 64]

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 4 Sequences and Series Miscellaneous Exercise 4 [Pages 63 - 64]

Miscellaneous Exercise 4 | Q 1 | Page 63

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

Miscellaneous Exercise 4 | Q 2 | Page 63

For a G.P. a = `4/3 and "t"_7 = 243/1024`, find the value of r.

Miscellaneous Exercise 4 | Q 3 | Page 64

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 4 | Q 4 | Page 64

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

Miscellaneous Exercise 4 | Q 5 | Page 64

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

Miscellaneous Exercise 4 | Q 6 | Page 64

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

Miscellaneous Exercise 4 | Q 7 | Page 64

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

Miscellaneous Exercise 4 | Q 8 | Page 64

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

Miscellaneous Exercise 4 | Q 9 | Page 64

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

Miscellaneous Exercise 4 | Q 10 | Page 64

Find \[\displaystyle\sum_{r=1}^{n}(5r^2 + 4r - 3)\].

Miscellaneous Exercise 4 | Q 11 | Page 64

Find \[\displaystyle\sum_{r=1}^{n}r(r-3)(r-2)\].

Miscellaneous Exercise 4 | Q 12 | Page 64

Find \[\displaystyle\sum_{r=1}^{n}\frac{1^2 + 2^2 + 3^2+...+r^2}{2r + 1}\]

Miscellaneous Exercise 4 | Q 13 | Page 64

Find \[\displaystyle\sum_{r=1}^{n}\frac{1^3 + 2^3 + 3^3 +...+r^3}{(r + 1)^2}\]

Miscellaneous Exercise 4 | Q 14 | Page 64

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

Miscellaneous Exercise 4 | Q 15 | Page 64

Find 122 + 132 + 142 + 152 + … + 202.

Miscellaneous Exercise 4 | Q 16 | Page 64

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

Miscellaneous Exercise 4 | Q 17 | Page 64

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

Miscellaneous Exercise 4 | Q 18 | Page 64

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

Miscellaneous Exercise 4 | Q 19 | Page 64

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.

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Chapter 4: Sequences and Series

Exercise 4.1Exercise 4.2Exercise 4.3Exercise 4.4Exercise 4.5Miscellaneous Exercise 4
Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board - Shaalaa.com

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 4 - Sequences and Series

Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 4 (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 1 (Commerce) 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 1 (Commerce) 11th Standard Maharashtra State Board chapter 4 Sequences and Series are Concept of Sequences, Geometric Progression (G.P.), General Term Or the nth Term of a G.P., Sum of the First n Terms of a G.P., Sum of Infinite Terms of a G. P., Recurring Decimals, Harmonic Progression (H. P.), Types of Means, Special Series (Sigma Notation).

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 4 Sequences and Series 11th extra questions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board and can use Shaalaa.com to keep it handy for your exam preparation

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