Question

Write the first five terms of each of the following sequence.
$a_1=-1,a_n=\frac{a_{n-1}}{n+2},n>1$ and $\forall nϵN$

Answer 1

Given $a_1=-1$ and $a_n=\frac{a_{n-1}}{n+2},n>1$
$a_2=\frac{a_1}{2+2}=-\frac{1}{4}$
$a_3=\frac{a_2}{3+2}=\frac{-\frac{1}{4}}{5}=-\frac{1}{20}$
$a_4=\frac{a_3}{4+2}=\frac{-\frac{1}{20}}{6}=-\frac{1}{120}$
$a_5=\frac{a_4}{5+2}=\frac{-\frac{1}{120}}{7}=-\frac{1}{840}$
Therefore, the required terms of the sequence are $-1,-\frac{1}{4},-\frac{1}{20},-\frac{1}{120}$ and $-\frac{1}{840}$.