In an A P the sum of the terms equidistant from the beginning and end is always same and - Maths - Sequences and Series

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

Ankush Jain · Accepted Answer

Let the first term of an A P be a and last term be l
and common difference between each term be d
âˆ´ A P = a, a+ d,
a + 2d, , l â€“ 2d,
l â€“ 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 â€“
pd = a + l (2)
(1) = (2) [Hence proved]

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.