Q.  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 .Please prove the above with each step properly written .

Asked by conveyrajat | 15th May, 2014, 11:52: AM

Expert Answer:

Let the first and the last terms of an AP are a and l respectively

Common difference = d, then we have

a, a + d, a + 2d, a + 3d .............. l - 3d, l - 2d, l - d, l

The sum of numbers equidistant from the beginning and the end, we get
a + 3d + l - 3d = a + l ... (i)
Sum of the first and last term = a + l ... (ii)

Thererfore, (i) = (ii)

Answered by Avinash Soni | 15th May, 2014, 12:14: PM