Question

Find the sum of first 51 terms of an A.P. whose 2^nd and 3^rd terms are 14 and 18 respectively.

Answer 1

Given, t₂ = 14 and t₃ = 18

`=>` d = t₃ – t₂

= 18 – 14

= 4

Now t₂ = 14

`=>` a + d = 14

`=>` a = 14 – 4

`=>` a = 10

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

∴ Sum of first 51 terms of an A.P. = `51/2 [2 xx 10 + 50 xx 4]`

= `51/2 [20 + 50 xx 4]`

= `51/2 [20 + 200]`

= `51/2 xx 220`

= 51 × 110

= 5610