Question

if an A.P consists of n terms with first term a and nth term L show that the sum of the mth term from the begining and the mth term from the end is (a+l).

NEEDED ANSWER WITH CORRECT EXPLANATION

Answer 1

Given :

First term of A.P is a

nth term =l

Let d be the common difference

nth term=a+(n-1)d

l=a+(n-1)d

d=l-a/n-1 ------------1

Mth term from the beginning

=a+(m-1)d=a+(m-1)(l-a/n-1 ) ----------------2

Mth term from the end we get:

where we consider first term as l and the common difference=-d

=l+(m-1)(-d)

=l+(m-1)x(-(l-a)/n-1)

=I-(m-1)(l-a)/n-1 --------------3

thus sum of mth term from beginning to end is

=a+(m-1)(l-a/n-1 ) +I-(m-1)(l-a)/n-1

=a+l

Hence proved