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.
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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
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
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