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

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

Solution:

First term, a = 10

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

$\Rightarrow \frac{14}{2}[2 \times 10+(14-1) d]=1505$

$\Rightarrow 7 \times(20-13 d)=1505$

$\Rightarrow 20-13 d=\frac{1505}{7}=215$

$\Rightarrow 13 d=-195$

$\Rightarrow d=-15$

Now,

$a_{25}=10+24(-15)=-350$