Chapter 12.1, Problem 43AYU

In Problems 37-50, a sequence is defined recursively. Write down the first five terms.

$a_1=3$; $a_n=\frac{a_{n-1}}{n}$

To determine

To find: The first five terms when a sequence is defined recursively.

Answer to Problem 43AYU

$a_1=\text{ 3},a_2=\frac{3}{2},a_3=\frac{3}{4},a_4=\frac{3}{8},a_5=\frac{3}{16}$

Explanation of Solution

Given:

$a_1=\text{ 3}$

Calculation:

$a_n=\frac{a_{n-1}}{n}$

It is given that $a_1=\text{ 3}$. We have if $n=2$.

$a_2=\frac{a_{2-1}}{2}$

$a_2=\frac{a_1}{2}=\frac{3}{2}$

$a_2=\frac{3}{2}$

If $n=3$ then,

$a_3=\frac{a_{\text{3 }-1}}{2}$

$a_3=\frac{a_2}{2}=\frac{3}{4}$

$a_3=\frac{3}{4}$

If $n=4$ then,

$a_4=\frac{a_{\text{4 }-1}}{2}$

$a_4=\frac{a_3}{2}$

$a_4=\frac{3}{8}$

If $n=5$ then,

$a_5=\frac{a_{\text{5 }-1}}{2}$

$a_5=\frac{a_4}{2}$

$a_5=\frac{3}{16}$