CBSE Class 10 Answered

Dear Student,

Say thetre are  n terms in AP series.

x th term from begining  =  a+(x-1)d                            (1)  

[  'a' is first term and  'd' is common difference ]

x th term from ending     = a+ [ (n+1 -x) -1]d              (2)

Sum of x th terms from begining and from ending = a+(x-1)d   +   a+ [ (n+1 -x) -1]d  = 2a+(n-1)d     (3)

n th term in the series = a+(n-1)d

Sum of first and last terms = a+   a+(n-1)d  =    2a+(n-1)d             (4)

Equation (3), (4) are equal.

So ,the sum of the terms equidistant from the beginning and the end is always same and equal to the sum of the first and last terms and it is  2a+(n-1)d

Regards

Topperlearning team