Maharashtra State Board Class 11 (FYJC / HSC) Commerce Mathematics & Statistics Solutions Chapter 4 Sequences and Series Ex 4.3 - Digest Answers | Maharashtra Board Solutions

Q: Question 1: Determine whether the sum to infinity of the following G.P’.s exist. If exists, find it. (i) (ii) (iii) (iv)

Step-by-step solution provided.

Q: Question 3: If the common ratio of a G.P. is and sum of its terms to infinity is 12. Find the first term.

r = , sum to infinity = 12 … [Given] Sum to infinity = ∴ 12 = ∴ a = 12 × ∴ a = 4

Q: Question 4: If the first term of a G.P. is 16 and sum of its terms to infinity is , find the common ratio.

a = 16, sum to infinity = … [Given] Sum to infinity = ∴ ∴ ∴ 11 – 11r = 5 ∴ 11r = 6 ∴ r =

Q: Question 5: 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.

Let the required G.P. be a, ar, ar2, ar3, ….. Sum to infinity of this G.P. = 5 ∴ 5 = ∴ a = 5(1 – r) ……(i) Also, the sum of the squares of the terms is 15.

Balbharati Maharashtra State Board11th Commerce Maths Solution Book PdfChapter 4 Sequences and Series Ex 4.3 Questions and Answers.

Maharashtra State Board 11th Commerce Maths Solutions Chapter 4 Sequences and Series Ex 4.3

Question 1 Maharashtra Board Solution

Determine whether the sum to infinity of the following G.P’.s exist. If exists, find it. (i) (ii) (iii) (iv)

Solution & Step-by-Step Answer:

Question 2 Maharashtra Board Solution

Express the following recurring decimals as a rational number. (i) (ii) 3.5 (iii) (iv) (v)

Solution & Step-by-Step Answer:

(i) = 0.323232….. = 0.32 + 0.0032 + 0.000032 + ….. Here, 0.32, 0.0032, 0.000032, … are in G.P. with a = 0.32 and r = 0.01 Since, |r| = |0.01| < 1 ∴ Sum to infinity exists. ∴ Sum to infinity =

(ii) 3.5 = 3.555… = 3 + 0.5 + 0.05 + 0.005 + …
Here, 0.5, 0.05, 0.005, … are in G.P. with a = 0.5 and r = 0.1
Since, |r| = |0.1| < 1
∴ Sum to infinity exists.

(iii) = 4.181818…..
= 4 + 0.18 + 0.0018 + 0.000018 + …..
Here, 0.18, 0.0018, 0.000018, … are in G.P. with a = 0.18 and r = 0.01
Since, |r| = |0.01| < 1
∴ Sum to infinity exists.

(iv) 0.345 = 0.3454545…..
= 0.3 + 0.045 + 0.00045 + 0.0000045 + …..
Here, 0.045, 0.00045, 0.0000045, … are in G.P. with a = 0.045, r = 0.01
Since, |r| = |0.01| < 1
∴ Sum to infinity exists.

(v) = 3.4565656 …..
= 3.4 + 0.056 + 0.00056 + 0.0000056 + ….
Here, 0.056, 0.00056, 0.0000056, … are in G.P. with a = 0.056 and r = 0.01
Since, |r| = |0.01| < 1
∴ Sum to infinity exists.

Question 3 Maharashtra Board Solution

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

Solution & Step-by-Step Answer:

r = , sum to infinity = 12 … [Given] Sum to infinity = ∴ 12 = ∴ a = 12 × ∴ a = 4

Question 4 Maharashtra Board Solution

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

Solution & Step-by-Step Answer:

a = 16, sum to infinity = … [Given] Sum to infinity = ∴ ∴ ∴ 11 – 11r = 5 ∴ 11r = 6 ∴ r =

Question 5 Maharashtra Board Solution

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.

Solution & Step-by-Step Answer:

Let the required G.P. be a, ar, ar2, ar3, ….. Sum to infinity of this G.P. = 5 ∴ 5 = ∴ a = 5(1 – r) ……(i) Also, the sum of the squares of the terms is 15.

Chapter 4 Sequences and Series Ex 4.3 Solutions