Question

In an arithmetic progression the sum of two terms equidistant from the beginning and the end is always _____ to the sum of the first and last terms.

• A. equal
• B. unequal
• C. different
• D. various

Answer 1

The correct option is A equal

Let $a$ be first term $d$ be common difference of an AP having $n$ number of terms.

So $m$th term from the beginning is, $a_m=a+(m-1)d$

and $m$ the term from end is $a_{n-m}=a+(n-1)d-(m-1)d=a+(n-m)d$

So $a_m+a_{n-m}=2a+(n-1)d=\left[a\right]+[a+(n-1\left)d\right]=$ sum of first and last term