JEE MAIN - Mathematics (2025 - 2nd April Evening Shift - No. 14)
The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by $\frac{21}{2}$. Then the number of terms which are integers in the A.P. is :
6
4
8
10
Explanation
Let the number of terms be $2 n$
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$$\begin{aligned} & n d=6 \\ & (a+(2 n+1) d)-a=\frac{21}{2} \\ & \Rightarrow 2 n d-d=\frac{21}{2} \\ & \Rightarrow 12-\frac{21}{2}=d \end{aligned}$$
$$\begin{aligned} & \Rightarrow d=\frac{3}{2} \\ & \therefore n=4 \\ & \therefore \text { Total terms }=8 \end{aligned}$$
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