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

Page / Exercise

## 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) Question 1(ii)

Find which of the following sequence form a G.P.: Solution 1(ii) Question 1(iii)

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

9, 12, 16, 24, …….

Solution 1(iii) Question 2

Find the 9th term of the series:

1, 4, 16, 64,……

Solution 2 Question 3

Find the seventh term of the G.P: Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6

Find the nth term of the series:

1, 2, 4, 8, ……..

Solution 6 Question 7 Solution 7 Question 8

Find the sixth term of the series:

22, 23, 24,………….

Solution 8 Question 9 Solution 9 Question 10

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

Solution 10 Question 11 Solution 11 Question 12

Find the next two terms of the series:

2, - 6, 18, - 54 ……

Solution 12

Given series: 2, - 6, 18, - 54 …… ## Chapter 11 - Geometric Progression Exercise Ex. 11(B)

Question 1 Solution 1 Question 2

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

Solution 2 Question 3 Solution 3 Question 4

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

Solution 4 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 Question 6

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

Solution 6 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 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 Question 9

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

Solution 9 Question 10

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

Solution 10 ## Chapter 11 - Geometric Progression Exercise Ex. 11(C)

Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 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 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 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 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 Question 8(i) Solution 8(i) Question 8(ii) Solution 8(ii) Question 9

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

Solution 9 ## 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) Question 1(ii)

Find the sum of G.P.:

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

Solution 1(ii) Question 1(iii)

Find the sum of G.P.: Solution 1(iii) Question 1(iv)

Find the sum of G.P.: Solution 1(iv) Question 1(v)

Find the sum of G.P.: Solution 1(v) Question 1(vi)

Find the sum of G.P.: Solution 1(vi) Question 2

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

Solution 2 Question 3 Solution 3 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 Question 5 Solution 5 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 Question 7

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

Solution 7 Question 8

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

Solution 8 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 Question 10 Solution 10 Question 11

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

Solution 11 Question 12(i)

Find the geometric mean between: Solution 12(i) Question 12(ii)

Find the geometric mean between: Solution 12(ii) Question 12(iii)

Find the geometric mean between:

2a and 8a3

Solution 12(iii) Question 13 Solution 13 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 Question 15

Find the 5th term of the G.P. Solution 15

First term (a) =  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 Question 17 Solution 17 Thus, the given sequence is a G.P. with  Question 18

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

Solution 18 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 Given, sum of first two terms = -4 And, 5th term = 4(3rd term)

ar2 = 4(a)

r2 = 4

r = ±2

When r = +2, When r = -2,  ### STUDY RESOURCES

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