The two APs have the same common difference. If the first terms of these APs are 3 and 8 respectively, what will be the difference between the sums of their first 50 terms?

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300

250

200

100

answer is B.

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Detailed Solution

Given that the two APs have same common difference and first term

a 1 = 8

and second term

a 2 = 3

.
Let

a 1 and a 2

be the first term of the two A.P.’s and d be the common difference of the two A.P.’s.
Let

S 50 and S 50 ′

be the sum of their first 50 terms.
Formula used for sum of first n term of A.P.:

S n = n 2 [2 a + (n − 1) d]

Determining the difference between the sums of their first 50 terms: Question Image

Therefore, the difference between the two sums is 250.
Hence, option (2) is correct.

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