Question

for a gp S3=21 & S6=189 find the first term and the common ratio​

Answer 1

Answer:

Let Sn 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

Sn=r−1a(rn−1)

Given :

S6=9×S3

S6=r−1a(r6−1)=9×r−1a(r3−1)

⇒r6−1=9(r3−1)

⇒(r3−1)(r3+1)=9(r3−1)

⇒r3=−1+9=8

⇒r=2