Grades 9/10/11 Sequences, Series, and Financial Literacy

Arithmetic and geometric sequences. Financial applications including simple interest, compound interest, and annuities.

This is one of seven strands of the CEMC Grade 9/10/11 courseware. The other strands and more information about this courseware is available on the Grade 9/10/11 homepage.

Unit 1: Representing Sequences

In this lesson, students will be introduced to sequences and the associated notation. They will develop an understanding of recursive sequences and represent sequences in a variety of ways.

In this lesson, we will be introduced to a famous pattern of numbers known as Pascal’s triangle. Patterns within Pascal’s triangle will be investigated, including those that assist in expanding powers of binomials, \((a+b)^n\). The Binomial Theorem will be used to expand binomials of the form \((a+b)^n\) and to find specific terms within a binomial expansion.

All of the pencil and paper practice exercises, answers, and solutions for this unit are reproduced here.

This is a collection of additional, and sometimes challenging, problems that extend the material covered in this unit, connect material from different lessons, and further explore real-world applications.

Unit 2: Arithmetic and Geometric Sequences and Series and Financial Applications

In this lesson, we will investigate arithmetic sequences. Arithmetic sequences will be described with a recursive formula and with a general term. The general term will be used to solve problems involving arithmetic sequences.

In this lesson, we will look at a variety of different investment options offered by banks or similar institutions. The relationship between simple interest and arithmetic sequences will be explored and simple interest problems will be solved.

In this lesson, we will investigate geometric sequences. Geometric sequences will be described with a recursive formula and with a general term. The general term will be used to solve problems involving geometric sequences. 

In this lesson, we will define compound interest, and relate it to geometric sequences and exponential growth.  The effect of different compounding periods will be investigated, and the formula for compound interest will be used to calculate future value, present value, the interest rate, or the number of compounding periods. 

In this lesson, the idea of a series is introduced. Two formulas to calculate the sum of the first ‌\(n\) terms of an arithmetic series will be developed and then applied in a variety of settings.

In this lesson, we will work with geometric series. The formula for the sum of the first ‌\(n\) terms in a geometric series will be developed and then applied in a variety of settings. 

In this lesson, annuities are studied as a financial application of geometric series. We will solve annuity problems using the geometric series formula and we will derive formulas for solving annuity problems. These formulas will be used to solve a variety of questions involving annuities.

In this lesson, we will use technology to solve a variety of different questions relating to annuities. This will include comparing annuities, solving problems involving multiple calculations, and looking at cases beyond ordinary simple annuities. 

In this lesson, we will explore other financial topics such as different types of employment income, income tax, and other deductions. We will also compare the options of buying, renting, and leasing. 

All of the pencil and paper practice exercises, answers, and solutions for this unit are reproduced here.

This is a collection of additional, and sometimes challenging, problems that extend the material covered in this unit, connect material from different lessons, and further explore real-world applications.