Question

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

Answer 1

Sum of n terms = $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
where a = first term d = common difference

therefore, $S_{14}=\frac{14}{2}[2\times 10+(14-1\left)d\right]=1505$

solve for d, we get, 215 = 20 + 13d
hence, d = 15.

now, $a_n=a+(n-1)d$
therefore,$a_{25}=10+(25-1)15$
$a_{25}=10+24\times 15=370.$