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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.
Solution
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.
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