Arithmetic Sequence Calculator - nth Term Sum Formula
Calculate the nth term, sum, and first 10 terms of an arithmetic sequence given the first term and common difference.
How to use this calculator
👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉
In plain English — what does this do?
🔢 This tool does the maths for you! Just type in your numbers, and it gives you the answer right away. No need to count on your fingers or use a pen and paper.
An arithmetic sequence (also called an arithmetic progression) is a sequence of numbers where each term after the first is obtained by adding a fixed value called the common difference. This calculator finds the nth term, the sum of the first n terms, and lists the first 10 terms.
nth Term (aₙ)
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Sum (Sₙ)
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First 10 Terms
What is Arithmetic Sequence Calculator - nth Term Sum Formula?
An arithmetic sequence (also called an arithmetic progression) is a sequence of numbers where each term after the first is obtained by adding a fixed value called the common difference. This calculator finds the nth term, the sum of the first n terms, and lists the first 10 terms.
How to use it
- 1️⃣ Enter the first term (a₁) of the sequence.
- 2️⃣ Enter the common difference (d) — positive for increasing, negative for decreasing.
- 3️⃣ Enter n — the term position you want to calculate.
- 4️⃣ The nth term, sum, and first 10 terms appear instantly.
Formula
💡 See it in action — a real example
❓ Common questions
- What is the common difference?
- The common difference d is the constant value added to each term to get the next. If d > 0 the sequence increases; if d < 0 it decreases; if d = 0 all terms are equal.
- Can d be a fraction or decimal?
- Yes. d can be any real number, including fractions and decimals. For example, a₁=1, d=0.5 gives 1, 1.5, 2, 2.5, …
- What is the sum of the first n natural numbers?
- This is an arithmetic sequence with a₁=1 and d=1. The sum is n(n+1)/2, a special case of the general formula.
- How is arithmetic sequence used in real life?
- Arithmetic sequences model situations with constant change: loan repayment schedules, salary increments, uniform motion distances, and staircase step heights.
- What is the difference between arithmetic and geometric sequences?
- Arithmetic sequences add a constant (d) each step. Geometric sequences multiply by a constant (r) each step. 2,4,6,8 is arithmetic (d=2); 2,4,8,16 is geometric (r=2).