Question

Two APs have the same common difference. If the first 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 two APs. 

Here, a₁ = 8 and a₂ = 3 

Suppose d be the common difference of the two APs

Let S₅₀ and S’₅₀ = `50/2 [2a_1 + (50 - 1)d] - 50/2 [2a_2 + (50 - 1)d]`

= 25(2 × 8 × 49d) – 25(2 × 3 + 49d)

= 25 × (16 – 6)

= 250

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