Question

the sum of first n terms of an ap is given by n ssuare+8n.find its 12th term

Answer 1

Sum of first n terms of the AP = n² + 8n
Sum of first 1 term = first term, a = 1² + 8×1 = 9
Sum of first 12 terms = 12² + 8×12 = 240

But we also know that sum of first n terms = (n/2)[a + an]
(an = nth term)

So sum of first 12 terms = (12/2)[9 + a₁₂]
⇒ 240 = 6×(9 + a₁₂)
⇒ 9 + a₁₂ = 240/6 = 40
⇒ a₁₂ = 40- 9 
⇒ a₁₂ = 31

12th term is 31.

Answer 2

We are supposed to find the 12th term of AP .

To find 12th term we need to subtract the sum of first 11 terms from sum of first 12 terms .

Substitute n = 12

Substitute n = 11

12th term =

12th term = 240-209

12th term = 31