Let `a_n` be the `n^(t h)` term of an A.P. If `sum_(r=1)^(100)a_(2r)=alpha&sum_(r=1)^(100)a_(2r-1)=beta,` then the common difference of the A.P. is `alpha-beta` (b) `beta-alpha` `(alpha-beta)/2` (d) None of these

Options

A. `(alpha-beta)/(200)`
B. `alpha-beta`
C. `(alpha-beta)/(100)`
D. `beta-alpha`

Explanation

To solve the problem, we need to analyze the given information about the arithmetic progression (A.P.) and the sums of its terms.

1. **Understanding the terms of the A.P.**:
Let the first term of the A.P. be \( a \) and the common difference be \( d \). The \( n^{th} \) term of the A.P. can be expressed as:
\[ a_n = a + (n-1)d \]

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