SELINA Solutions for Class 10 Maths Chapter 11 - Geometric Progression

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