Question

The sum of the first n terms of an AP is given by Sn = (3n² – n). Find its

(i) nth term,

(ii) first term and

(iii) common difference.

Answer 1

S_n = 3n² – n

S₁ = 3(1)² – 1 = 3 – 1 = 2

S₂ = 3(2)² – 2 = 12 – 2 = 10

a₁ = 2

a₂ = 10 – 2 = 8

(i) a_n = a + (n – 1) d

= 2 + (n – 1) x 6

= 2 + 6n – 6

= 6n – 4

(ii) First term = 2

(iii) Common difference = 8 – 2 = 6