Question

If for a a G.P. r=1/3 and a=g, ts​

Answer 1

Step-by-step explanation:

For a G.P a

n

=a

1

r

n−1

where r is common ratio.

Given that a

n

=96

⇒3×r

n−1

=96

⇒r

n−1

=32

⇒r

n

=32r [Let this be equation 1]

Also, sum of the first n terms of a finite G.P. is given by S

n

=

r−1

a

1

(r

n

−1)

⇒

r−1

3(32r−1)

=189

⇒32r−1=63r−63

⇒31r=62

⇒r=2

Putting r=2 in equation 1,we get

⇒2

n

=64

⇒n=6