# 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
${u}_{n}={u}_{1}+\left(n\u20131\right)d$
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 $y=a\times {b}^{n}$ to understand geometric series.

2. Sketch the graph of quadratics of the form
$y=a{n}^{2}+bn$
to understand the sum to *n *terms of an arithmetic series. e.g.