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

a1= 0.23

r=0.01

:)

Explanation:

Answer 2

`a_1=0.23` and
`r=0.1`.

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=(a_2)/(a_1)=(0.23(0.1))/(0.23)=0.1`

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