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

Question

asked Jul 21, 2021 81.3k views

1 Answer

HoffZ · Answer 1 · 2021-07-25T01:29:59+0000

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

So, for example, you might choose

y=2x+3

Which will produce the following sequence:

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

and so on