Question

Write the first five terms of the sequence, whose $n^{th}$ term is $a_n=n(n+2)$.

Answer 1

Finding sequence.
Given, $a_n=n(n+2),n\in N$
Substituing $n=1,2,3,4$ and $5$ in $a_n$, we get
$a_1=1\times (1+2)$
$\Rightarrow a_1=1\times 3$
$\Rightarrow a_1=3$

$a_2=2\times (2+2)$
$\Rightarrow a_2=2\times 4$
$\Rightarrow a_2=8$

$a_3=3\times (3+2)$
$\Rightarrow a_3=3\times 5$
$\Rightarrow a_3=15$

$a_4=4\times (4+2)$
$\Rightarrow a_4=4\times 6$
$\Rightarrow a_4=24$

$a_5=5\times (5+2)$
$\Rightarrow a_5=5\times 7$
$\Rightarrow a_5=35$

Hence, the first five terms of the sequence are $3,8,15,24$ and $35$.