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