Find the indicated terms in each of the sequences in where $n^{t h}$ terms are :

$a_{n} = \frac{n (n - 2)}{n + 3}; a_{20}$

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Solution

Here, $a_{n} = \frac{n (n - 2)}{n + 3}$

Putting n =20, we have

$a_{20} = \frac{20 (20 - 2)}{20 + 3} = \frac{20 \times 18}{23} = \frac{360}{23}$

Thus, the $20^{t h}$ term of wequence is $\frac{360}{23} .$

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