Arithmetic sequence term
An arithmetic sequence changes by adding the same number each time. To find a specific term, you need to track the starting term and the common difference.
Method
- Identify the first term and the common difference.
- Count how many steps away the requested term is from the first term.
- Add the difference repeatedly, or use the pattern:
- 2nd term = first term + 1 difference
- 3rd term = first term + 2 differences
- and so on.
- Simplify the result carefully.
Example pattern
If the sequence starts at 5 and increases by 3, the terms go:
5, 8, 11, 14, ...
So each new term is found by adding 3 again.
Check your answer
- Make sure the difference between consecutive terms stays constant.
- Substitute your term back into the pattern to see whether it fits.
- If the answer is exact, leave it in simplified form.
Common mistake
Do not multiply when the sequence is arithmetic; the rule is repeated addition of the same difference.