Question

Find the indicated term in the sequence, whose $n^{th}$ term is: $a_n=\frac{n(n-2)}{n+3};a_{20}$

Answer 1

Finding $a_{20}$ term of sequence.
Given, $a_n=\frac{n(n-2)}{n+3}$
Substituting $n=20$ in $a_n$, we get
$\Rightarrow a_{20}=\frac{20(20-2)}{(20+3)}$
$\Rightarrow a_{20}=\frac{20\times 18}{23}$
$\Rightarrow a_{20}=\frac{360}{23}$

Hence, the value of $a_{20}$ term of sequence is $\frac{360}{23}$.