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 + ….. + 2^n-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 4^th term. Find its 7^th 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 5^th and the 6^th 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 8^th 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, 5^th term = 4(3^rd term)

⇒ ar² = 4(a)

⇒ r² = 4

⇒ r = ±2

When r = +2,

 

When r = -2,