Arithmetic Sequence Calculator
The arithmetic sequence calculator finds the nᵗʰ term and the sum of a sequence with a common difference.
Term 1048
Sum of the first 10255
Common difference5
Mean of the terms25.5the average of the first and last
Directionincreasing
Terms
| n | Term |
|---|---|
| 1 | 3 |
| 2 | 8 |
| 3 | 13 |
| 4 | 18 |
| 5 | 23 |
| 6 | 28 |
| 7 | 33 |
| 8 | 38 |
| 9 | 43 |
| 10 | 48 |
The formula
aₙ = a₁ + (n−1)d, Sₙ = n⁄2 (2a₁ + (n−1)d)
Gauss’s trick for the sum
Pair the first term with the last, the second with the second-to-last, and so on: every pair has the same total. That gives Sₙ = n × (first + last) ÷ 2 — the count times the average of the ends. It is the reason 1 + 2 + … + 100 is 50 × 101 = 5,050.