Show that 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.

Explanation

To show that in an Arithmetic Progression (A.P.), the sum of the terms equidistant from the beginning and the end is always the same and equal to the sum of the first and last terms, we can follow these steps:

### Step-by-Step Solution

1. **Define the A.P.**:
Let the first term of the A.P. be \( A_1 \) and the common difference be \( d \). The \( n \)-th term of the A.P. can be expressed as:
\[
A_n = A_1 + (n-1)d
...