Question

Prove that the sum of an odd number of terms in A.P. is equal to the middle term multiplied by the number of terms. ​

Answer 1

Answer:

Let the AP be a,a+d,a+2d,...

The Sum of terms = 2n(2a+(n−1)d)

=an+2n(n−1)d

Let there are n terms in the AP and n is an odd integer.

Hence, the middle term is (2n+1)th term=a+(2n+1−1)d=a+2(n−1)d

Hence, multiplying n to the middle term would b equal to sum of terms.