Let the sum of an infinite G . P . , whose first term is a and the common ratio is r , be 5 . Let the sum of…

Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be 9825. Then the sum of the first 21 terms of an AP, whose first term is 10ar, nth term is an and the common difference is 10ar2, is equal to
  1. 21a11
  2. 22a11
  3. 15a16
  4. 14a16

Solution

For the infinite G.P. 

S∞=a1-r=5

Also a+ar+ar2+ar3+ar4=5

⇒a1-r51-r=9825

i.e. 1-r5=98125⇒r5=3353⇒r=3535

Now S21=21220ar+21-110ar2

=2110ar+100ar2

=21·a11

Asked in: JEE Main 2022 (27 Jul Shift 2)

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