Arithmetic Sequence Calculator
Arithmetic sequence calculator
Find nth term and partial sum for arithmetic progressions.
Result
a12 = 37
Sum of first 12 terms = 246.
Auto
math
Flow
- Enter first term, common difference, and term index.
- Read nth term and cumulative sum instantly.
- Adjust n to compare sequence growth over different horizons.
Example
Worked example: a1 = 4, d = 3, n = 12
- 1 a12 = 4 + (12 - 1) × 3 = 37
- 2 S12 = 12/2 × [2×4 + 11×3]
- 3 S12 = 6 × 41 = 246
The 12th term is 37 and the first-12-term sum is 246.
How
- Enter first term, common difference, and term index.
- Read nth term and cumulative sum instantly.
- Adjust n to compare sequence growth over different horizons.
Avoid
- Confusing arithmetic difference with geometric ratio.
- Using n = 0 when formulas assume n starts at 1.
- Applying nth-term formula when d is not constant.
Checks
Best fit
Arithmetic Sequence Calculator is built for compute nth term and partial sum for arithmetic progressions with constant difference. If Arithmetic Sequence Calculator does not match the input scope, compare the answer with a second method.
Input check
Match the entered values to this rule before copying the answer: an = a1 + (n - 1)d, Sn = n/2 × [2a1 + (n - 1)d].
Sanity check
For Arithmetic Sequence Calculator, use the worked example as a quick benchmark: The 12th term is 37 and the first-12-term sum is 246. If the arithmetic sequence calculator answer is far away, check whether an input, unit, or mode changed.
Before copying
Review this common issue first: confusing arithmetic difference with geometric ratio.
FAQ
What makes a sequence arithmetic?
Successive terms differ by a constant amount d.
Can d be negative?
Yes. Negative d produces a decreasing arithmetic sequence.
Does this also return the sequence list?
This tool focuses on nth term and sum outputs for clean workflow speed.
Switch
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