Question

The sum of the first n terms of an A.P. is represented by S_n = 6n − n². Find the common difference.

Answer 1

The sum of the first n terms of an A.P is S_n = 6n − n².

Putting n = 1,

S₁ = 6 × 1 − 1²

= 6 − 1

= 5 

Putting n = 2,

S₂ = 6 × 2 − 2²

= 12 − 4

= 8

a₁ = 5 = a

∴ S₂ = 2a + d

 8 = 2 × 5 + d

8 = 10 + d

d = 8 − 10

∴ d = −2