Question

If $s=n(5n-3)$ for all values of $n$, find the $p^{th}$ term.

Answer 1

$S_n=n(5n-3)$

$S_1=a=1(5-3)=2$

$S_n=\frac{n}{2}\{2a+(n-1\left)d\right\}$

$S_n=\frac{n}{2}\{a+a+(n-1\left)d\right\}$

$S_n=\frac{n}{2}\{a+a_n\}$

$n(5n-3)=\frac{n}{2}\{2+a_n\}$

$10n-6=2+a_n$ $a_n=10n-8$

$\Rightarrow a_p=10p-8$

So the $p^{th}$ term is $10p-8$