Question

Answer the following 13,10,7,4,...what is its explicit equation

Answer 1

This is an arithmetic sequence.

The numbers differ by a constant.

The general form of an arithmetic sequence is:

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

Where

a is first term

n is nth term

d is the common difference

Looking at the sequence, we can say the common difference is -3 [since 3 is subtracted from a term to get the next term]

Also, first term is 13

Now, we plug into formula:

$\begin{gathered} a_n=a+(n-1)d \\ a_n=13+(n-1)(-3) \\ a_n=13-3n+3_{} \\ a_n=16-3n \end{gathered}$