An arithmetic sequence has a constant difference between consecutive terms: a₁, a₁+d, a₁+2d, ... The nth term: aₙ = a₁ + (n−1)d. The sum of first n terms: Sₙ = n/2 × (first + last) = n/2 × (2a₁ + (n−1)d).
How to Use
Enter sequence parameters:
- First term (a₁): Starting value
- Common difference (d): Gap between terms
- n: Number of terms
Formulas
- aₙ = a₁ + (n−1)d
- Sₙ = n/2 × (2a₁ + (n−1)d)
- d = a₂ − a₁
- n = (aₙ − a₁)/d + 1
Examples
Sequence 2,5,8,11,14: a₁=2, d=3. 10th term: 2+9×3=29. Sum of 10 terms: 10/2×(2+29)=155.
Step-by-Step Instructions
- 1Enter the first term.
- 2Enter the common difference.
- 3Set number of terms.
- 4View the nth term and sum.
- 5See the full sequence.