Question

The following geometric arrays suggest a sequence of numbers.
(a) Find the next two terms.
(b) Find the ${100}^{th}$ term.
(c) Find the $n^{th}$ term.

Answer 1

So, $T_5=T_4+10=20+10=30=5\times 6$
$T_6=T_5+12=30+12=42=6\times \mathrm{7....}$
$T_{100}=100\times 101=10,100$
$T_n=n\times (n+1)=n^2+n$.