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

1.	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» 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

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»

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