Question

The sum of first n terms of an A.P. is 2n² + 13n. Find its n^th term and hence 10^th term.

Answer 1

Given: S_n = 2n² + 13n

Find S_{n – 1}:

S_{n – 1} = 2(n – 1)² + 13(n – 1)

S_{n – 1} = 2(n² – 2n + 1) + 13n – 13

S_{n – 1} = 2n² – 4n + 2 + 13n – 13

S_{n – 1} = 2n² + 9n – 11

Calculate a_n:

a_n = S_n – S_{n – 1}

a_n = (2n² + 13n) – (2n² + 9n – 11)

a_n = 2n² + 13n – 2n² – 9n + 11

a_n = 4n + 11

Find 10^th term (a₁₀):

a₁₀ = 4(10) + 11

a₁₀ = 40 + 11

a₁₀ = 51

The n^th term is 4n + 11 and the 10^th term is 51.