Arithmetic
Explicit Models
Example 3
Find the explicit model for the following sequence:
5, 9, 13, 17, 21 …
Step 1. Determine the common difference.
9 - 5 = 4
13 - 9 = 4
Every difference is four, d = 4.
Step 2. Substitute d = 4 and a = 5 into the formula and simplify.
an = 5 + 4(n - 1)
an = 5 + 4n - 4
an = 4n + 1