The sum of first third & seventeenth terms of an A.P.is 216 .Find the sum of the first 13 terms Of an A.P.

1 thought on “The sum of first third & seventeenth terms of an A.P.is 216 .Find the sum of the first 13 terms Of an A.P.”

1. Answer:

   sum of the first 13 terms of the given AP = 936

   Step-by-step explanation:

   we know, nth term of an AP , tₙ = a+(n-1)d

   => 1st term = a ;

   3rd term =a+2d ;

   17th term = a+16d;

   Given that,

   a+(a+2d)+(a+16d)=216

   3a+18d = 216

   3(a+6d) = 216

   a+6d = 216/3

   a+6d = 72 ——— (1)

   Sum of “n” terms of an AP, Sₙ = (n/2) [2a+(n-1)d]

   => S₁₃ = (13/2)[2a+12d]

   = (13/2)[2(a+6d)]

   = 13(a+6d)

   = 13*72 [ by (1) ]

   = 936

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