Question

If the sum of $p$ terms of an $AP$ is $3p^2+4p$, find it's nth term.

Answer 1

nth term = pth term - (p-1)th term

$=3p^2+4p-\left[3\right(p-1{)}^2+4(p-1)]$

$=3p^2+4p-\left[3\right(p^2+1-2p)+4p-4]$

$=3p^2+4p-[3p^2+3-6p+4p-4]$

$=3p^2+4p-3p^2-3+6p-4p+4$

$=6p+1$

Hence the nth term.