It is expected that students will:

• derive and apply expressions to represent general terms and sums for geometric growth and to solve problems

Determine the term and the sum of the first n terms of the geometric sequence whose first three terms are 2, 6, and 18.

Mathematicians use sigma notation as a way to write the sum of a series. For example: .
Use sigma notation to write the series
5 - 15 + 45 - . . . + 3645.

*Suppose that a principal of P dollars is invested at an annual interest rate r that is compounded annually. The amount A after t years is given by .

For the geometric series , find the sum of 20 terms.

*The time needed for an investment to double in value can be estimated using the rule of 72, which states that where i is the annual percentage interest rate and n the number of years.

• connect geometric sequences to exponential functions over the natural numbers

The world's population grows by 2% per year. The world food production can sustain an additional 200 million people per year. In 1987 the population was 5 billion, and food production could sustain 6 billion people.

*The following is a school trip telephoning tree.

• estimate values of expressions for infinite geometric processes

For the inifinite series , estimate the sum to four decimal places.

An oil well produces 25 000 barrels of oil during its first month of production. If its production drops by 5% each month, estimate the total production before the well runs dry.