免费等差数列计算器
计算等差数列的第n项、公差和前n项和。
Nth Term
48.0000
平均值25.5000
公式
## Arithmetic Sequence ### nth Term **aₙ = a₁ + (n - 1) × d** ### Sum of n Terms **Sₙ = n/2 × (2a₁ + (n-1)d)** or equivalently: **Sₙ = n/2 × (a₁ + aₙ)** An arithmetic sequence has a constant difference between consecutive terms.
计算示例
Arithmetic sequence: first term = 3, common difference = 5, find the 10th term and sum.
- 01a₁₀ = 3 + (10-1) × 5 = 3 + 45 = 48
- 02Sum = 10/2 × (3 + 48) = 5 × 51 = 255
常见问题
What is an arithmetic sequence?
An arithmetic sequence has a constant difference between consecutive terms. Examples: 2,5,8,11,14... (d=3) or 100,90,80,70... (d=-10).
How do I find the common difference?
Subtract any term from the next term: d = a₂ - a₁. If this value is constant throughout, it is an arithmetic sequence.
What is the sum formula?
Sₙ = n/2 × (first + last). This is the number of terms times the average of the first and last terms.
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