Question

What is the pattern to the sequence -21,-51,-81,-111,-141?

Answer 1

The sequence is:

-21,-51,-81,-111,-141:

You need to find the difference between each term:

`\begin{gathered} -51-(-21)=-30 \\ -81-(-51)=-30 \\ -111-(-81)=-30 \\ -141-(-111)=-30 \end{gathered}`

The difference is -30.

You use the next formula to get the pattern:

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

Where

an: pattern

a1: first term of the sequence

d: difference

`\begin{gathered} a_n=-21+(-30)(n-1) \\ a_n=-21-30(n-1) \\ a_n=-21-30n+30 \\ a_n=-30n+9 \end{gathered}`

Then, the sequence follows the pattern:

`a_n=-30n+9`