Given:
a+ar+ar2+ar3+......∞=15
⇒1−ra=15....(1)
And,
a2+a2r2+a2r4+a2r6+......∞=150
⇒1−r2a2=150
⇒(1+ra)(1−ra)=150
⇒(1+r)a=10...(2)
Solving equation (1) and (2), we get
r=51⇒a=12
Now,
ar2+ar4+ar6......∞
=1−r2ar2=1−25112×251=21
If the sum of an infinite GP, a,ar,ar2,ar3,… is 15 and the sum of the squares of its each term is 150, then the sum of ar,2ar4,ar6,… is:
Held on 26 Aug 2021 · Verified 6 Jul 2026.
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