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Sum of Arithmetic Sequence Calculator

Online arithmetic series calculator: enter first term, difference and n to sum the first n terms.

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S_n=n(a₁+a_n)/2
First
Difference
Positive integer

📖 Tutorial | Arithmetic Sum

1. Definition
The sum is S_n=n(a₁+a_n)/2=na₁+n(n−1)d/2, from pairing first with last (Gauss).
2. Formula & Notation
S_nSum of n terms
3. Properties & Laws
  • Pairing formula;
  • a₁,d formula;
  • Quadratic in n;
  • Gauss: 1+…+100=5050.
4. Steps
  1. Enter a₁, d, n;
  2. Click "Sum";
  3. Or click "Load Example".
5. Worked Examples
Example: 1+…+100 gives 5050.
6. Common Pitfalls
Choose the right formula;
n(n−1)/2, not n²/2;
n is a positive integer.

❓ FAQ | Arithmetic Sum

Formula?
n(a₁+a_n)/2.
Only a₁,d?
na₁+n(n−1)d/2.
Gauss?
5050.
Shape?
Quadratic.
Why /2?
n/2 pairs.
No last term?
Use the term formula.
Reverse-add?
Derivation.