An arithmetic sequence has a constant difference between consecutive terms. This difference is called the common difference (d).
To find the nth term of a linear sequence:
1. Find the common difference — this is the coefficient of n.
2. Work out what to add to get the first term.
Example: 5, 8, 11, 14, …
Common difference = 3, so it starts with 3n.
When n = 1: 3(1) = 3, but the first term is 5, so add 2.
nth term = 3n + 2.
To check if a value belongs to the sequence, set it equal to the nth term and solve for n. If n is a positive whole number, it's in the sequence.
Is 50 in the sequence 3n + 2?
3n + 2 = 50 → 3n = 48 → n = 16. Yes, it's the 16th term ✓