Question

Prove that the half of the sum of first and last term of an A.P. is equal to middle term of an A.P. if A.P. consists odd number of terms.

Answer 1

let first term be a
let last term be L
L = a + (n-1)d
(L + a)2:-
(a + (n-1)d + a)/2
(2a + (n-1)d)/2
2a/2 + [(n-1)d]/2
a + [(n-1)d]/2
= middle term