# How do you find the first five terms of the given sequence?

Apr 15, 2018

${a}_{1} = 1$, ${a}_{2} = \frac{1}{2}$, ${a}_{3} = \frac{1}{6}$, ${a}_{4} = \frac{1}{24}$, ${a}_{5} = \frac{1}{120}$

#### Explanation:

${a}_{1} = 1$

${a}_{n} = \frac{1}{n} {a}_{n - 1}$

For $n = 2$

${a}_{2} = \frac{1}{2} {a}_{1} = \frac{1}{2} \left(1\right) = \frac{1}{2}$

For $n = 3$

${a}_{3} = \frac{1}{3} {a}_{2} = \frac{1}{3} \left(\frac{1}{2}\right) = \frac{1}{6}$

For $n = 4$

${a}_{4} = \frac{1}{4} {a}_{1} = \frac{1}{4} \left(\frac{1}{6}\right) = \frac{1}{24}$

For $n = 5$

${a}_{5} = \frac{1}{5} {a}_{4} = \frac{1}{5} \left(\frac{1}{24}\right) = \frac{1}{120}$

Note that the closed form solution to this recursive relation is

a_n=1/(n!)