Answer
$\frac{4}{5},\frac{15}{17},\frac{12}{13},\frac{35}{37},\frac{24}{25}$
Work Step by Step
$a_{n}=\frac{n^{2}-1}{n^{2}+1}$ for $n\geq 3$
Rewrite the formula:
$a_n=\dfrac{(n+2)^2-1}{(n+2)^2+1}$ for $n\geq 1$
Substitute $1,2,3,4,5$ to $n$:
$a_{1}=\frac{3^{2}-1}{3^{2}+1}=\frac{8}{10}=\frac{4}{5}$
$a_{2}=\frac{4^{2}-1}{4^{2}+1}=\frac{15}{17}$
$a_{3}=\frac{5^{2}-1}{5^{2}+1}=\frac{24}{26}=\frac{12}{13}$
$a_{4}=\frac{6^{2}-1}{6^{2}+1}=\frac{35}{37}$
$a_{5}=\frac{7^{2}-1}{7^{2}+1}=\frac{48}{50}=\frac{24}{25}$
