Question

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.

Answer 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