Arithmetic Sequence Calculator
aₙ = a₁ + (n−1)d. Find any term of an arithmetic sequence.
Result
a10
32.0000
Sum of first 10 terms: 185.00.
- First term a₁5
- Common diff d3
- Term number n10
- Term aₙ32.0000
- Sum 1..n185.00
- First 5 terms5, 8, 11, 14, 17
Step-by-step
- aₙ = a₁ + (n−1)d = 5 + (10−1) × 3 = 32.0000.
- Sₙ = (n/2)(a₁ + aₙ) = (10/2)(5 + 32.00) = 185.00.
How to use this calculator
- Enter first term and common difference.
- Pick term number n.
- Read aₙ + sum.
About this calculator
Arithmetic sequence: each term differs from the previous by a constant d. Formula aₙ = a₁ + (n−1)d. Sum of first n terms: Sₙ = (n/2)(a₁ + aₙ). Examples: even numbers (a₁=2, d=2), powers-of-2 indices (a₁=1, d=1), or stair-step seating arrangements. Common in counting problems and discrete math.
Frequently asked
Arithmetic: constant difference (d). Geometric: constant ratio (r). Different families.
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