Question

The sum of the terms equidistant from the beginning and end in an A.P. is always same and is equal to the sum of and terms.

Answer 1

Let first term $=a$,

Last term $=l$

The $n^{th}$ term of an $A.P$. can be expressed as:

$a_n=a+(n-1)d{n}^{t}h$ term from the beginning $=a+(n-1)d\dots \left(i\right)$

$n^{th}$ term from the end $=l+(n-1)(-d)\dots \left(ii\right)$

Adding equation (i) & (ii)

$=a+(n-1)d+l+(n-1)(-d)$

$=a+l$

Therefore, the sum of the terms equidistant from the beginning and end in an A.P. is always same and equal to $a+l$ i.e., sum of first and last terms