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