# SELINA Solutions for Class 10 Maths Chapter 11 - Geometric Progression

Revise Selina Solutions for ICSE Class 10 Mathematics Chapter 11 Geometric Progression at TopperLearning. Study the solutions to understand if a given sequence can form a geometric progression (GP) or not. As per the Math question, learn to work with a GP to find a specific term in a sequence.

By studying the textbook solutions, you will also gain an understanding of how to apply GP concepts to solve real problems. To enhance your Maths capabilities, attempt our ICSE Class 10 Maths online practice tests and self-assess your conceptual clarity. Our revision notes and video lessons can also be used for getting a grip on the basics of GP.

## Chapter 11 - Geometric Progression Exercise Ex. 11(A)

Find which of the following sequence form a G.P.:

8, 24, 72, 216………

Find which of the following sequence form a G.P.:

Find which of the following sequence form a G.P.:

9, 12, 16, 24, …….

Find
the 9^{th} term of the series:

1, 4, 16, 64,……

Find the seventh term of the G.P:

Find the nth term of the series:

1, 2, 4, 8, ……..

Find the sixth term of the series:

2^{2}, 2^{3}, 2^{4},………….

Find the G.P. whose first term is 64 and next term is 32.

Find the next two terms of the series:

2, - 6, 18, - 54 ……

Given series: 2, - 6, 18, - 54 ……

## Chapter 11 - Geometric Progression Exercise Ex. 11(B)

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

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

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

Find the geometric progression with 4^{th}
term = 54 and 7^{th} term = 1458.

Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P.is positive.

The fourth term, the seventh term and the last term of a geometric progression are 10, 80 and 2560 respectively. Find its first term, common ratio and number of terms.

If the 4^{th} and 9^{th}
terms of a G.P. are 54 and 13122 respectively, find its general term.

The fifth, eight and eleventh terms of a
geometric progression are p, q and r respectively. Show that: q^{2} =
pr

## Chapter 11 - Geometric Progression Exercise Ex. 11(C)

If for a G.P., p^{th},
q^{th} and r^{th}
terms are a, b and c respectively; prove that:

(q - r) log a + (r - p) log b + (p - q) log c = 0

If a, b and c are in G.P., prove that:

log a, log b and log c are in A.P.

If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.

If a, b and c are in A.P, a, x, b are in G.P. whereas b, y and c are also in G.P.

Show
that: x^{2}, b^{2}, y^{2} are in A.P.

If a, b and c are in A.P. and also in G.P., show that: a = b = c.

## Chapter 11 - Geometric Progression Exercise Ex. 11(D)

Find the sum of G.P.:

1 + 3 + 9 + 27 + ………. to 12 terms

Find the sum of G.P.:

0.3 + 0.03 + 0.003 + 0.0003 +….. to 8 items.

Find the sum of G.P.:

Find the sum of G.P.:

Find the sum of G.P.:

Find the sum of G.P.:

How many terms of the geometric progression 1 + 4 + 16 + 64 + …….. must be added to get sum equal to 5461?

A boy spends Rs.10 on first day, Rs.20 on second day, Rs.40 on third day and so on. Find how much, in all, will he spend in 12 days?

A geometric progression has common ratio = 3 and last term = 486. If the sum of its terms is 728; find its first term.

Find the sum of G.P.: 3, 6, 12, …… 1536.

How many terms of the series 2 + 6 + 18 + …………… must be taken to make the sum equal to 728?

In a G.P., the ratio between the sum of first three terms and that of the first six terms is 125 : 152. Find its common ratio.

If the sum of 1+ 2 + 2^{2} + …..
+ 2^{n-1} is 255,find the value of n.

Find the geometric mean between:

Find the geometric mean between:

Find the geometric mean between:

2a
and 8a^{3}

The first term of a G.P. is -3 and the
square of the second term is equal to its 4^{th} term. Find its 7^{th}
term.

Find the 5th term of the G.P.

First term (a) =

The first two terms of a G.P. are
125 and 25 respectively. Find the 5^{th} and the 6^{th} terms
of the G.P.

First term (a) = 125

Thus, the given sequence is a G.P. with

The first term of a G.P. is 27. If
the 8^{th} term be , what will be the sum of 10 terms?

Find a G.P. for which the sum of first two terms is -4 and the fifth term is 4 times the third term.

Let the five terms of the given G.P. be

Given, sum of first two terms = -4

And, 5^{th} term
= 4(3^{rd} term)

⇒ ar^{2}
= 4(a)

⇒ r^{2}
= 4

⇒ r = ±2

When r = +2,

When r = -2,

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