# Chapter 11 : Geometric Progression - Selina Solutions for Class 10 Maths ICSE

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## Chapter 11 - Geometric Progression Excercise 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 ……

## Chapter 11 - Geometric Progression Excercise 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 Excercise 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 Excercise 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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