Question

Find the ${18}^{th}$ and ${25}^{th}$ terms of the sequence defined by
$a_n=\{\begin{array}{cc}n(n+3),& ifnϵN\text{and n is even}\\ \frac{2n}{n^2+1},& ifnϵN\text{and n is odd.}\end{array}$

Answer 1

$n=18=even{a}_{18}=18\left(21\right)=378n=25=odd{a}_{25}=\frac{2\times 25}{{25}^2+1}=\frac{50}{626}$