Problems on finding the G.P. when certain terms or conditions are given are included in this exercise. For any clarifications on how to solve problems of this chapter and others, students can refer to the Selina Solutions for Class 10 Maths anytime. It is a vital resource for exam preparations. Further, the solutions to this exercise can be accessed in the Concise Selina Solutions for Class 10 Maths Chapter 11 Geometric Progression Exercise 11(B) PDF, which is given in the links below.

## Selina Solutions Concise Maths Class 10 Chapter 11 Geometric Progression Exercise 11(B) Download PDF

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### Access Selina Solutions Concise Maths Class 10 Chapter 11 Geometric Progression Exercise 11(B)

**1. Which term of the G.P. :**

**Solution: **

In the given G.P.

First term, a = -10

Common ratio, r = (5/âˆš3)/ (-10) = 1/(-2âˆš3)

We know that, the general term is

t_{n} = ar^{n â€“ 1}

So,

t_{n} = (-10)( 1/(-2âˆš3))^{n â€“ 1} = -5/72

Now, equating the exponents we have

n â€“ 1 = 4

n = 5

Thus, the 5^{th} of the given G.P. is -5/72

**2. The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression. **

**Solution:**

Given,

t_{5} = 81 and t_{2} = 24

We know that, the general term is

t_{n} = ar^{n â€“ 1}

So,

t_{5} = ar^{5 â€“ 1} = ar^{4} = 81 â€¦. (1)

And,

t_{2} = ar^{2 â€“ 1} = ar^{1} = 24 â€¦. (2)

Dividing (1) by (2), we have

ar^{4}/ ar = 81/ 24

r^{3} = 27/ 8

r = 3/2

Using r in (2), we get

a(3/2) = 24

a = 16

Hence, the G.P. is

16, 24, 36, 54, â€¦â€¦

**3. Fourth and seventh terms of a G.P. are 1/18 and -1/486 respectively. Find the G.P. **

**Solution: **

Given,

t_{4} = 1/18 and t_{7} = -1/486

We know that, the general term is

t_{n} = ar^{n â€“ 1}

So,

t_{4} = ar^{4 â€“ 1} = ar^{3} = 1/18 â€¦. (1)

And,

t_{7} = ar^{7 â€“ 1} = ar^{6} = -1/486 â€¦. (2)

Dividing (2) by (1), we have

ar^{6}/ ar^{3} = (-1/486)/ (1/18)

r^{3} = -1/27

r = -1/3

Using r in (1), we get

a(-1/3)^{3} = 1/18

a = -27/ 18 = -3/2

Hence, the G.P. is

-3/2, -3/2(-1/3), -3/2(-1/3)^{2}, -3/2(-1/3)^{3}, â€¦â€¦

-3/2, 1/2, -1/6, 1/18, â€¦..

**4. If the first and the third terms of a G.P are 2 and 8 respectively, find its second term. **

**Solution:**

Given,

t_{1} = 2 and t_{3} = 8

We know that, the general term is

t_{n} = ar^{n â€“ 1}

So,

t_{1} = ar^{1 â€“ 1} = a = 2 â€¦. (1)

And,

t_{3} = ar^{3 â€“ 1} = ar^{2} = 8 â€¦. (2)

Dividing (2) by (1), we have

ar^{2}/ a = 8/ 2

r^{2} = 4

r = Â± 2

Hence, the 2^{nd} term of the G.P. is

When a = 2 and r = 2 is 2(2) = 4

Or when a = 2 and r = -2 is 2(-2) = -4

**5. The product of 3 ^{rd}Â and 8^{th}Â terms of a G.P. is 243. If its 4^{th}Â term is 3, find its 7^{th}Â term**

**Solution: **

Given,

Product of 3^{rd}Â and 8^{th}Â terms of a G.P. is 243

The general term of a G.P. with first term a and common ratio r is given by,

t_{n} = ar^{n â€“ 1}

So,

t_{3} x t_{8 }= ar^{3 â€“ 1} x ar^{8 â€“ 1} = ar^{2} x ar^{7 }= a^{2}r^{9} = 243

Also given,

t_{4} = ar^{4 â€“ 1} = ar^{3} = 3

Now,

a^{2}r^{9} = (ar^{3}) ar^{6} = 243

(3) ar^{6} = 243

ar^{6} = 81

ar^{7 â€“ 1} = 81 = t_{7}

Thus, the 7^{th} term of the G.P is 81.