Question

Which expression defines the arithmetic series 4 + 8+ 12 + . . . for four terms?

Answer 1

We can see that

d = 8 - 4 = 4

d = 12 - 8 = 4

...

So d is a constant of the arithmetic series.

Then the 4th term would be

$a_4=12+4=16$

Then we get:

$\begin{gathered} a_n=a_1+(n-1)d \\ a_n=4+(n-1)4 \\ a_n=4+4n-4 \\ a_n=4n\text{ n = 1, 2, 3, 4} \end{gathered}$

Then our final answer will be:

$a_n=4n\text{ n=1, 2, 3, 4}$