NZ Level 7 (NZC) Level 2 (NCEA)
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.

a

Express the first decimal place, $0.8$0.8 as an unsimplified fraction.

b

Express the second decimal place, $0.08$0.08 as an unsimplified fraction.

c

Hence write, using fractions, the first five terms of the geometric sequence representing $0.8888\dots$0.8888

d

State the values of $a$a, the first term, and $r$r, the common ratio, of this sequence.

$a$a$=$=$\editable{}$

$r$r$=$=$\editable{}$

e

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.

Easy
Approx 4 minutes

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 sum $0.25+0.0025+0.000025+\text{. . .}$0.25+0.0025+0.000025+. . .

### Outcomes

#### M7-3

Use arithmetic and geometric sequences and series

#### 91258

Apply sequences and series in solving problems