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

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

a – b = 100 d ̃ d = α−β100\frac{\alpha - \beta}{100}