Question

Two APs have the same common difference if the first terms of the APs be 3 and 9 respectively.Find the difference between their first 50 terms​

Answer 1

Step-by-step explanation:

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

and

Let s30ands′50=502[2a1+(50-1)d]-502[2a2+(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.