Arithmetic sequences grow by adding the same amount each step, like 3, 7, 11, 15, …
How to use the Arithmetic Sequence Calculator
- First term (a₁)
- Common difference (d)
- Term number (n)
Results update as you type, and every field accepts the units shown in its menu.
How it works
Multiply the common difference by n − 1 and add the first term. The sum averages the first and last terms and multiplies by n.
Inputs explained
| Field | What to enter |
|---|---|
| First term (a₁) | A number |
| Common difference (d) | A number |
| Term number (n) | A number |
What each result means
- nth term = [First term (a₁)] + ([Term number (n)] – 1)×[Common difference (d)]
- Sum of first n terms = [Term number (n)]×([First term (a₁)] + [nth term])÷2
Example values
How the main result changes when First term changes and everything else stays at the example values above:
| First term (a₁) | nth term |
|---|---|
| 1.5 | 77.5 |
| 2.25 | 78.25 |
| 3 | 79 |
| 3.75 | 79.75 |
| 4.5 | 80.5 |
| 6 | 82 |
Formula
aₙ = a₁ + (n − 1)dSₙ = n(a₁ + aₙ) ÷ 2Worked example
Inputs — First term (a₁): 3; Common difference (d): 4; Term number (n): 20.
Results — nth term = 79; Sum of first n terms = 820.
Key terms
- Common difference
- The fixed amount added to get the next term.
Frequently asked questions
How did Gauss add 1 to 100?
Pairing terms: 50 pairs each summing to 101 gives 5,050.
Can d be negative?
Yes, the sequence then decreases.
What formula does the Arithmetic Sequence Calculator use?
aₙ = a₁ + (n − 1)d.