Find the first 5 terms of the sequence, defined by
Question:

Find the first 5 terms of the sequence, defined by

$a_{1}=-1, a_{n}=$ $\frac{a_{n-1}}{n}$ for $n \geq 2$

Solution:

To Find: First five terms of a given sequence

Condition: n ≥ 2

$a_{1}=-1, a_{n}=\frac{a_{n-1}}{n}$ for $n \geq 2$

Put $n=2$ in $n^{\text {th }}$ term (i.e. $a_{n}$ ), we have

$a_{2}=\frac{(-1)}{2}\left(\right.$ as $\left.a_{1}=-1\right)$

Put $n=3$ in $n^{\text {th }}$ term $\left(\right.$ i.e. $\left.a_{n}\right)$, we have

$a_{3}=\frac{(-1)}{6}\left(\operatorname{as} a_{2}=\frac{(-1)}{2}\right)$

Put $n=4$ in $n^{\text {th }}$ term (i.e. $a_{n}$ ), we have

$a_{4}=\frac{(-1)}{24}\left(a s a_{3}=\frac{(-1)}{6}\right)$

Put $n=5$ in $n^{\text {th }}$ term (i.e. $a_{n}$ ), we have

$a_{5}=\frac{(-1)}{120}\left(\operatorname{as} a_{3}=\frac{(-1)}{24}\right)$

First five terms of a given sequence are $-1, \frac{(-1)}{2}, \frac{(-1)}{6}, \frac{(-1)}{24}, \frac{(-1)}{120}$