Activity – Sequences and Series

1. To understand the concept of arithmetic sequence sketch the graph of some linear functions using some graphing software ( I used DESMOS). You will observe that when n=1, 2, 3, ..... the y-values will change increase/decrease with a constant number. Try to link it with the general term of an arithmetic sequence  un=u1+n1d and draw the conclusion that the coefficient of n represents the common difference and also the gradient of the line. Here is an example

You can sketch exponential functions of the form  y= a ×bn to understand geometric series.

2. Sketch the graph of quadratics of the form  y=an2+bn to understand the sum to terms of an arithmetic series. e.g.