Question

Repeated decimals can be written as an infinite geometric series to help convert them to a fraction. Consider the repeating decimal below.
0.232323… = 0.23 + 0.23(0.01) + 0.23(0.01)2 + …
What is a1?
What is r?

Answer 1

Answer:

a1= 0.23

r=0.01

:)

Step-by-step explanation:

Answer 2

Answer:

$a_1=0.23$ and $r=0.1$.

Step-by-step explanation:

It is given that Repeated decimals can be written as an infinite geometric series to help convert them to a fraction.  

Consider the repeating decimal below.

$0.232323…=0.23+0.23(0.01)+0.23(0.01)^2+…$

We need to find the value of $a_1\text{ and }r$.

$a_1$ is the first term of the series. So,

$a_1=0.23$

$r$ is the common ratio of the series. So,

$r=\dfrac{a_2}{a_1}=\dfrac{0.23(0.1)}{0.23}=0.1$

Therefore, $a_1=0.23$ and $r=0.1$.