Question

The sum of n terms of an A.P. is 3n² + 5n. Find the A.P. Hence, find its 16th term.

Answer 1

S_n = 3n² + 5n

Taking n = 1, we get

S₁ = 3(1)² + 5(1)

⇒ S₁ = 3 + 5

⇒ S₁ = 8

⇒ a₁ = 8

Taking n = 2, we get

S₂ = 3(2)² + 5(2)

⇒ S₂ = 12 + 10

⇒ S₂ = 22

∴ a₂ = S₂ – S₁ = 22 – 8 = 14

Taking n = 3, we get

S₃ = 3(3)² + 5(3)

⇒ S₃ = 27 + 15

⇒ S₃ = 42

∴ a₃ = S₃ – S₂ = 42 – 22 = 20

So, a = 8,

d = a₂ – a₁ = 14 – 8 = 6

Now, we have to find the 15^th term

a_n = a + (n – 1)d

a₁₆ = 8 + (16 – 1)6

a₁₆ = 8 + 15 × 6

a₁₆ = 8 + 90

a₁₆ = 98

Hence, the 16^th term is 98.