1. Does each term increase/decrease by the same added amount each time?
Any term minus its previous term should get the same value which is the common difference.

2. Show that the sequence is arithmetic
Show that the sequence is arithmetic. List the first term and the common difference. d = an – an-1 a term minus the previous term.
(a) 4, 2, 0, -2, . . .
What are the first four terms of example (b)
a1 = 3 a2 = = 7 a3 = = 11 a4 = 15

3. Find the twenty fourth term of the arithmetic sequence:
–3, 0, 3, 6, . . .
d = 0 – (-3)
an = n – 3
an = 3n – 6

4. The difference in the terms values divided by the difference in the number of terms gets d.
Use elimination to get rid of a1 and solve for d.
After you find d you can plug it back into one of the equations and find a1 (the first term)
This is the recursive formula now use this to find the formula for the nth term.