The number of terms of an A.P is even .The sum of the odd terms is 24, and that of the even terms 30, and the last term exceeds the first by $10 \frac{1}{2}$ . Find the number of terms.

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Solution

Let $n$ be the total number of terms, $d$ be the common difference, a be the first term.
The difference between the sums of odd and even terms is thus $\frac{n d}{2} = 30 - 24 = 6$
So, $n d = 12$
Also, last term = $a + (n - 1) d = 10.5 + a$
$\Rightarrow n d - d = 10.5$
$\Rightarrow d = 1.5$ and so, $n = 8$

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