Arithmetic Sequence Calculator
The nth term and the sum of the first n terms of an arithmetic progression.
Results
Term at position n
98.0000
Sum of the first n terms
1010.0000
Mean (average)
50.5000
What this tool does
An arithmetic sequence adds the same amount at every step, which makes it the right model for equal instalments, fixed annual increases or rows of seats that grow by a constant number. Set the first term, the step and the position you want.
Formula
aₙ = a₁ + (n−1)d , Sₙ = n ÷ 2 × (2a₁ + (n−1)d)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
a | First term | — |
d | Common difference | — |
n | Position n | — |
AN | Term at position n | — |
SN | Sum of the first n terms | — |
AV | Mean (average) | — |
Worked example
- First term3
- Common difference5
- Position n20
- Term at position n98.0000
- Sum of the first n terms1010.0000
- Mean (average)50.5000
Limitations
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.