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Question: Let a<sub>n</sub> be the n<sup>th</sup> term of an A.P. If \(\sum_{r = 1}^{100}a_{2r}\)= a&\(\sum_{r...

Let an be the nth term of an A.P. If ∑r=1100a2r\sum_{r = 1}^{100}a_{2r}= a&∑r=1100a2r−1\sum_{r = 1}^{100}a_{2r - 1}= b, then the common difference of the A.P. is

A

a – b

B

b – a

C

α−β2\frac{\alpha - \beta}{2}

D

None of these

Answer

None of these

Explanation

Solution

a1 + a3 + a5 +……+ a199 = b

a2 + a4 + a6 +……. + a200 = a

a2 –a1 + a4 – a3 + a6 – a5, ……..+ a200 – a199 = a – b

d + d + d +……+ d = a – b

d = α−β100\frac{\alpha - \beta}{100}