Question

Find the sum of 28 terms of an A.P. whose n^th term is 8n – 5.

Answer 1

n^th term of an A.P. = t_n = 8n – 5

Let a be the first term and d be the common difference of this A.P.

Then,

a = t₁

= 8 × 1 – 5

= 8 – 5

= 3

t₂ = 8 × 2 – 5

= 16 – 5

= 11

∴ d = t₂ – t₁

= 11 – 3

= 8

The sum of n terms of an A.P. = `S = n/2 [2a + (n - 1)d]`

`=>` Sum of 28 terms of an A.P. = `28/2 [2 xx 3 + 27 xx 8]`

= 14[6 + 216]

= 14 × 222

= 3108