Solution

Pattern Rule: Start at \(6\) and add \(1\) each time.

The pattern rule has its limitations:

• It is wordy.
• It is recursive:

e.g., to find the \(5^{th}\) term, you need to find the \(4^{th}\) term, to find the \(4^{th}\) term, you need to find the \(3^{rd}\) term, and so on.

Instead of using the pattern rule, we can describe the relationship between the term number and the term itself.

This is another way to describe a pattern.

\(6, ~7, ~8,~ 9, \ldots\)

General Term:term number \(+~5\)

How did we come up with the general term of this sequence?

Pattern Rule: Start at \(6\) and add \(1\) each time.

 \(6,\class{hl2}{\overset{+1}{\longrightarrow}} 7, \class{hl2}{\overset{+1}{\longrightarrow}} 8,\class{hl2}{\overset{+1}{\longrightarrow}} 9, \ldots\)