Chapter 12.1, Problem 41AYU

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

$a_1=5$; $a_n=2a_{n-1}$

To determine

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

Answer to Problem 41AYU

$a_1=5,a_2=10,a_3=20,a_4=40,a_5=80$

Explanation of Solution

Given:

$a_1=5$

Calculation:

$a_n=2a_{n-1}$

It is given that $a_1=5$. We have if $n=2$.

$a_2=2a_{2-1}$

$a_2=2a_1=2\left(5\right)=10$

$a_2=10$

If $n=3$ then,

$a_3=2a_{3-1}$

$a_3=2a_2=2\left(10\right)=20$

$a_3=20$

If $n=4$ then,

$a_4=2a_{4-1}$

$a_4=2a_3=2\left(20\right)=40$

$a_4=40$

If $n=5$ then,

$a_5=2a_{5-1}$

$a_5=2a_4=2\left(40\right)=80$

$a_5=80$