Chapter 12.1, Problem 43AYU

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

$a_1=1$; $a_2=2$; $a_n=a_{n-1}\cdot a_{n-2}$

To determine

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

Answer to Problem 43AYU

$a_1=\text{ 1},a_2=\text{ 2},a_3=\text{ 2},a_4=\text{ 4},a_5=\text{ 8}$

Explanation of Solution

Given:

$a_1=\text{ 1, }{a}_2=\text{ 2}$

Calculation:

$a_n=a_{n-1}*a_{n-2}$

It is given that $a_1=\text{ 1, }{a}_2=\text{ 2}$. We have if $n=\text{ 3}$.

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

$a_3=a_2*a_1$

$a_3=\text{ 2 }*\text{ 1 = 2}$

$a_3=\text{ 2}$

If $n=\text{ 4}$ then,

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

$a_4=a_3*a_2$

$a_4=\text{ 2 }*\text{ 2 = 4}$

$a_4=\text{ 4}$

If $n=\text{ 5}$ then,

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

$a_5=a_4*a_3$

$a_5=\text{ 4 }*\text{ 2 = 8}$

$a_5=\text{ 8}$