Question

the common ratio, last term and sum of all terms of a G.P are 3, 486 and 728 respectively. find the first term and the number of terms​

Answer 1

Step-by-step explanation:

a,ar,ar2 , ar3 , ........................arn−1 be the G. P.

Sn be sum first n terms of G.P

Let common ratio =r

and let an be the nth term of G.P

Given that r=3, last term i.e an=arn−1=486

Sn=r−1a(rn−1)=r−1rarn−1−a=728

Substituting the vlues in above eqn.

3−1(3)×486−a=728

(3)×486−2×728=a

First term i.e. a=2