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Progressions: Finding Common Difference of an AP
Sum of first 25 terms of an AP is 525; sum of the next 25 terms is 725; what is the common difference?
Correct Choice is (1) and Correct Answer is 8/25
The sum of the first 25 terms, S25 = 525
The sum of the next 25 terms, K25 = sum of next 25 terms = 725
a26 = a1 + 25d
a27 = a2 + 25d
K25 = a26 + a27 + ...... + a50
Or K25 = a1 + 25d + a2 + 25d + ...... + a25+ 25d
Or K25 = a1 + a2 + ...... + a25+ 25(25d)
Or K25 = S25 + 25(25d)
i.e., 725 = 525 + 25 x 25d
200 = 25 x 25d
8 = 25d
d = 8/25