Question

In an A.P. the sum of the terms equidistant from the beginning and end is always same and equal to the sum of first and last terms.

Answer 1

Let the first term of an A.P be a and last term be l and common difference between each term be d.

∴ A.P = a, a+ d, a + 2d, ............, l – 2d, l – d, l

New, sum of first and last term = a + l ...... (1)

Suppose, sum of any two numbers equidistant from the beginning and end of given A.P. (say p terms from the two ends)

= a + pd + l – pd = a + l ...... (2)

(1) = (2) [Hence proved]