Question

Consider the following list of entries: 0, 3, 6, 9, 12, 15, …. what’s the next entry?

Answer 1

We have the next list of entries:

0, 3, 6, 9, 12, 15, ….

And we must find the next entry

To find it we must use the formula for arithmetic sequence

$a_n=a_1+(n-1)d$

Where,

$\begin{gathered} a_1\colon\text{ first term} \\ d\colon\text{ common difference} \\ a_n\colon\text{ nth term} \end{gathered}$

In our case,

$\begin{gathered} a_1=0 \\ d=3-0=3 \end{gathered}$

The next entry will be the 7th term

So, we must find a7

$\begin{gathered} a_7=0+(7-1)\cdot3 \\ a_7=0+18 \\ a_7=18 \end{gathered}$

ANSWER:

The next entry is 18.