Question

Write a linear equation to describe the number pattern that starts with 3 and continues with positive odd integers.

Answer 1

In order to have a linear equation, you have to write an equation like

$y=mx+q$

The sequence has to start with 3, so we must choose $q=3$, because this guarantees that when $x=0$ we have

$y=0\cdot m + 3 =3$

Now, $m$ must be even. In fact, if $m$ is even, $mx$ will always be even for every possible $x$, and $mx+3$ will be odd.

So, for example, you might choose

$y=2x+3$

Which will produce the following sequence:

$\begin{array}{c|c}x&f(x)\\0&3\\1&5\\2&7\\3&9\end{array}$

and so on