Question

Sum of the first 14 terms of an A.P. is 1505 and its first term is 10. Find its 25^th term.

Answer 1

First term, a = 10

Sum of first 14 terms, $S_{14}=1505$

$$\begin{gathered} \Rightarrow \frac{14}{2}\left[2\times 10+\left(14-1\right)d\right]=1505 \\ \Rightarrow 7\times \left(20-13d\right)=1505 \\ \Rightarrow 20-13d=\frac{1505}{7}=215 \\ \Rightarrow 13d=-195 \\ \Rightarrow d=-15 \end{gathered}$$

Now,
$a_{25}=10+24\left(-15\right)=-350$