#### Answer

$a_{1}=1;a_{2}=\dfrac {7}{6};a_{3}=1;a_{4}=\dfrac {5}{6};a_{5}=\dfrac {19}{27}$

#### Work Step by Step

$a_{1}=\dfrac {4\times 1-1}{1^{2}+2}=1;$
$a_{2}=\dfrac {4\times 2-1}{2^{2}+2}=\dfrac {7}{6};$
$a_{3}=\dfrac {4\times 3-1}{3^{2}+2}=1$
$a_{4}=\dfrac {4\times 4-1}{4^{2}+2}=\dfrac {15}{18}=\dfrac {5}{6};$
$a_{5}=\dfrac {4\times 5-1}{5^{2}+2}=\dfrac {19}{27}$