If there are `(2n+1)` terms in A.P., then prove that the ratio of the sum of odd terms and the sum of even terms is `(n+1): ndot`

Explanation

There are (2n +1) terms in an arithmetic series.

Let `a , a + d , a + 2d , a + 3d , a + 4d ....... + a + (2n +1-1)d`

Here, odd terms are : `a , a + 2d , a + 4d , a + 6d , ...... a + 2nd`

Let number of odd terms = r and common difference = 2d

`Tr = a + (r - 1)2d`

`a + 2nd = a + (r - 1)2d`

`2nd/2d = r - 1`

`r = n + 1`

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