Applications of Geometric Series
Interactive practice questions
The recurring decimal $0.8888\dots$0.8888… can be expressed as a fraction when viewed as an infinite geometric series.
Express the first decimal place, $0.8$0.8 as an unsimplified fraction.
Express the second decimal place, $0.08$0.08 as an unsimplified fraction.
Hence write, using fractions, the first five terms of the geometric sequence representing $0.8888\dots$0.8888…
State the values of $a$a, the first term, and $r$r, the common ratio, of this sequence.
$a$a$=$=$\editable{}$
$r$r$=$=$\editable{}$
If we add up infinitely many terms of this sequence, we will have the fraction equivalent of our recurring decimal. Calculate the infinite sum of the sequence as a fraction.
The decimal $0.6666$0.6666$...$... can be expressed as a fraction.
The recurring decimal $0.444444\dots$0.444444… can be expressed as a fraction when viewed as an infinite geometric series.
Consider the number $0.252525$0.252525$\ldots$…