Question

Two Aps have the same common difference. If the fist terms of these Aps be 3 and 8 respectively. Find the difference between the sums of their first 50 terms.

Answer 1

Let a₁ and a₂ be the first terms of the two APs. 

Here, a₁ = 8 and a₂ = 3 

Suppose d be the common difference of the two Aps

`Let   s_30 and s' _50 = 50/2 [ 2a_1 + (50-1) d] - 50/2 [2a_2 + (50-1) d]`

= 25( 2 × 8 × 49d) - 25 (2 x 3 +49 d)

= 25 ×  (16-6)

= 250

Hence, the required difference between the two sums is 250.