Question

How many terms of G.P. 3, 3 2 , 3 3 , … are needed to give the sum 120?

Answer 1

The given G.P. is 3, 3 2 , 3 3 …

Let the first term and common ratio of the given G.P. be a and r respectively.

Let n terms be needed to obtain the sum as 120.

Here,

a=3 r= 3 2 3 =3

Here, r>1

The formula for the sum of first n terms of a G.P. for r>1 is given by,

S n = a( r n −1 ) r−1

Substitute the values of a and rin equation (1) to obtain the n th term.

120= 3( 3 n −1 ) 3−1 120= 3( 3 n −1 ) 2 120×2 3 =( 3 n −1 ) 3 n −1=80

Further simplify the above expression.

3 n =81 3 n = 3 4

Equate the power to obtain the value of n on both sides.

n=4

Thus, four terms are required to obtain the sum as 120.