Question

Find the first term and the common difference of an AP if the sum of first n terms is n(5n+7)/12

Answer 1

Given:

Sum of n terms of an arithmetic progression (AP) = n(5n+7)/ 12

To find:

The first term and common difference of the AP.

Solution:

Sum of first n terms = n(5n+7)/12 = 5n²/12 + 7n/12

We know that sum of n terms in an AP:

S = n/2[2a + (n-1)d]

=an + n²d/2 - nd/2

Comparing this equation with the given sum of n terms we get:

d = 5/6

The first term can be found out by putting n=1:

a1 = 1*(5*1 + 7)/12 = 1

Therefore the first term is 1 and the common difference is 5/6.