Question

if the sum of first n terms of an AP is an2 + bn, find its common difference

Answer 1

Sn = an² + bn

a1 = S1

S1 = a( 1 )² + b

S1 = a + b

a1 = a + b

a2 = S2 - S1

S2 = a ( 2 )² + 2b

S2 = 4a + 2b

a2 = 4a + 2b - a - b

a2 = 3a + b

d ( common difference ) = a2 - a1

3a + b - a - b

2a


d = 2a