Question

If the 8^th term of an A.P. is 37 and the 15^th term is 15 more than the 12^th term, find the A.P. Also, find the sum of first 20 terms of A.P.

Answer 1

For an A.P.

t₈ = 37

`=>` a + 7d = 37   ...(i)

Also, t₁₅ – t₁₂ = 15

`=>` (a + 14d) – (a + 11d) = 15

`=>` a + 14d – a – 11d = 15

`=>` 3d = 15

`=>` d = 5

Substituting d = 5 in (i), we get

a + 7 × 5 = 37

`=>` a + 35 = 37

`=>` a = 2

∴ Required A.P. = a, a + d, a + 2d, a + 3d, .....

= 2, 7, 12, 17, .....

Sum of the first 20 terms of this A.P.

= `20/2 [2 xx 2 + 19 xx 5]`

= 10[4 + 95]

= 10 × 99

= 990