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.

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

Question 1(i)

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

8, 24, 72, 216………

Solution 1(i)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 1(ii)

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

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 1(ii)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 1(iii)

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

9, 12, 16, 24, …….

Solution 1(iii)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 2

Find the 9th term of the series:

1, 4, 16, 64,……

Solution 2

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 3

Find the seventh term of the G.P:

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression 

Solution 3

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 4

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 4

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 5

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 5

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 6

Find the nth term of the series:

1, 2, 4, 8, ……..

Solution 6

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 7

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 7

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 8

Find the sixth term of the series:

22, 23, 24,………….

Solution 8

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 9

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 9

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 10

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

Solution 10

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 11

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 11

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 12

Find the next two terms of the series:

2, - 6, 18, - 54 ……

Solution 12

Given series: 2, - 6, 18, - 54 ……

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

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

Question 1

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 1

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 2

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

Solution 2

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 3

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 3

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 4

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

Solution 4

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 5

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

Solution 5

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 6

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

Solution 6

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 7

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.

Solution 7

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 8

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.

Solution 8

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 9

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

Solution 9

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 10

The fifth, eight and eleventh terms of a geometric progression are p, q and r respectively. Show that: q2 = pr

Solution 10

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

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

Question 1

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 1

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 2

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 2

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 3

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 3

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 4

If for a G.P., pth, qth and rth terms are a, b and c respectively; prove that:

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

Solution 4

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 5

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

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

Solution 5

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 6

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

Solution 6

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 7

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: x2, b2, y2 are in A.P.

Solution 7

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 8(i)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 8(i)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 8(ii)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 8(ii)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 9

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

Solution 9

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

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

Question 1(i)

Find the sum of G.P.:

1 + 3 + 9 + 27 + ………. to 12 terms

Solution 1(i)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 1(ii)

Find the sum of G.P.:

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

Solution 1(ii)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 1(iii)

Find the sum of G.P.:

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 1(iii)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 1(iv)

Find the sum of G.P.:

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 1(iv)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 1(v)

Find the sum of G.P.:

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 1(v)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 1(vi)

Find the sum of G.P.:

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 1(vi)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 2

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

Solution 2

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 3

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 3

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 4

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?

Solution 4

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 5

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 5

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 6

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

Solution 6

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 7

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

Solution 7

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 8

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

Solution 8

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 9

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.

Solution 9

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 10

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 10

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 11

If the sum of 1+ 2 + 22 + ….. + 2n-1 is 255,find the value of n.

Solution 11

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 12(i)

Find the geometric mean between:

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 12(i)

 Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 12(ii)

Find the geometric mean between:

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 12(ii)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 12(iii)

Find the geometric mean between:

2a and 8a3

Solution 12(iii)

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 13

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 13

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 14

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

Solution 14

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Question 15

Find the 5th term of the G.P. Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 15

First term (a) = Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression 

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression 

Question 16

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

Solution 16

First term (a) = 125 

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression 

Question 17

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression

Solution 17

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression 

Thus, the given sequence is a G.P. with Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression 

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression 

Question 18

The first term of a G.P. is 27. If the 8th term be Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression, what will be the sum of 10 terms?

Solution 18

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression 

Question 19

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

Solution 19

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

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression 

Given, sum of first two terms = -4

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression 

And, 5th term = 4(3rd term)

ar2 = 4(a)

r2 = 4

r = ±2

When r = +2,

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression 

When r = -2,

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression 

Selina Solutions Icse Class 10 Mathematics Chapter - Geometric Progression