The number of terms of an A.P.

Question

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 :

Accepted Answer

Let the number of terms be $2 n$

$$\begin{aligned}
& n d=6 \
& (a+(2 n+1) d)-a=\frac{21}{2} \
& \Rightarrow 2 n d-d=\frac{21}{2} \
& \Rightarrow 12-\frac{21}{2}=d
\end{aligned}$$

$$\begin{aligned}
& \Rightarrow d=\frac{3}{2} \
& \therefore n=4 \
& \therefore \text { Total terms }=8
\end{aligned}$$

Solutions · 1