Q.

If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is :

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a

16

b

15

c

14

d

17

answer is A.

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Detailed Solution

Given that the first term of arithmetic progression is a=3S25=S40−S252⋅S25=S402⋅2522a+24d=4022a+39d256+24d=206+39d1501+4d=602+13dCancel out the common factor 15 from both sides of the above equation 10+40d=8+52d12d=2d=16 Therefore, the common difference is d=1 6
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