If the sum of the first n terms of an A.P. is , then find its term. Hence write its 20th term.

Question

Philoid · Accepted Answer

We know that sum of n terms of an A.P. is given by,

Where a= first term, d= Common difference, n= No. of terms

⇒

⇒ 3n² + 7n=2an + (n-1)nd

⇒ 3n² + 7n=n²d + (2a-d)n

By comparing, we get

d=3,

2a-d=7

⇒ 2a-3=7

⇒ 2a=10

⇒ a=5

So, nth term of this A.P.,

A_n=a + (n-1)d=5 + (n-1)3=5 + 3n-3=3n + 2

So,nth term is given by (3n + 2)

Now,For 20^th term, n=20

A₂₀=3 × 20 + 2=62

If the sum of the first n terms of an A.P. is , then find its term. Hence write its 20^th term.