New Zealand
Level 7 - NCEA Level 2

# Applications of Geometric Progressions

## Interactive practice questions

Suppose you save $\$1$$1 the first day of a month, \2$$2 the second day, $\$4$$4 the third day, \8$$8 the fourth day, and so on. That is, each day you save twice as much as you did the day before.

a

What will you put aside for savings on the $17$17th day of the month?

b

What will you put aside for savings on the $29$29th day of the month?

Easy
Approx 3 minutes

Suppose you save $\$1$$1 the first day of a month, \2$$2 the second day, $\$4$$4 the third day, \8$$8 the fourth day, and so on. That is, each day you save twice as much as you did the day before.

A car enthusiast purchases a vintage car for $\$220000$$220000. Each year, its value increases at a rate of 1212 percent of its value at the beginning of the year. Find its value after 77 years, to two decimal places. Average annual salaries are expected to increase by 55 percent each year. If the average annual salary this year is found to be \49000$$49000:

### Outcomes

#### M7-3

Use arithmetic and geometric sequences and series

#### 91258

Apply sequences and series in solving problems