Question

The sum of first n terms of an AP is given by S_n = 3n² + 2n. Find the AP.

Answer 1

S_n = 3n² + 2n

S₁ = 3 × 1² + 2 × 1

= 3 + 2 = 5

a₁ = 5

S₂ = 3 × 2² + 2 × 2

= 3 × 4 + 4

12 + 4 = 16

a₁ + a₂ = 16

5 + a₂ = 16

a₂ = 16 − 5

a₂ = 11

d = a₂ − a₁ = 11 − 5 = 6 

a₁ = 5

a₂ = a + d = 5 + 6 = 11

a₃ = a + 2d = 5 + 2 × 6 = 17

a₄ = a + 3d = 5 + 3 × 6 = 23

Hence, 5, 11, 17, 23, ...., are in AP