Question

ithe sum of first, third and seventeenth term of an ap is 216. find the sum of the first 13 term of the ap.

Answer 1

nth term of an A.P whose starting term is "a" and common difference is "d"
is an = a+(n-1)d

1st term = a   3rd term =a+2d  17th term = a+16d

According to question 

a+a+2d+a+16d=216

3a+18d=216

3(a+6d) = 216

a+6d= 216/3

a+6d= 72

Sum of "n" terms in an AP = n(2a+(n-1)d)/2

Sum of thirteen terms =13(2a+12d)/2 
=13(a+6d)
= 13*72
= 936

Answer 2

(a)+(a+2)+(a+16d)=216
3a+18d=216
3(a+6d)=216
a+6d=72-------(i)
sum of nth term =n(2a+(n-1)d)/2
13 term =13(2a+12d)/2
=13×2(a+6d)/2
=13(a+6d)
=13×72 ( from eq i)
=936
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