• Problem:
What is the rule of 18, 21, 24?
• Answer:
The given sequence has a common difference of 3, thus, an arithmetic one. Common difference can be obtained when you subtract a term by its preceding term, 24 - 21 = 3 and 21 - 18 = 3 in which 3 is the common difference.
To formulate a rule for the given sequence, we'll use the formula for arithmetic sequence.
[tex]\large\boxed{\begin{array}{}\tt a_n=a_1+(n-1)d \\ \tt a_n= 18+(n-1)(3) \\ \tt a_n= 18 + 3n - 3 \\ \purple{\tt a_n=3n +15}\end{array}}[/tex]
• Thus, the rule for the given sequence is 3n + 15.
