Question

19. The sum of the first 3 terms of a geometric
progression (GP) is 9A, while the sum of the first
6 terms of the GP is 6A. The sum of the first
9 terms of the GP is
(A) 7A
(B) 8A
(C) 9A
(D) 10A​

Answer 1

Answer:

Let S

n

be sum first n terms of G.P. and r be common ratio

Formula for sum of n terms of G.P. is given by

S

n

=

r−1

a(r

n

−1)

Given :

S

6

=9×S

3

S

6

=

r−1

a(r

6

−1)

=9×

r−1

a(r

3

−1)

⇒r

6

−1=9(r

3

−1)

⇒(r

3

−1)(r

3

+1)=9(r

3

−1)

⇒r

3

=−1+9=8

⇒r=2