Summation Of Series Calculator
Last updated: June 2026 · Free · No sign-up required
Enter values above and click Calculate to see your result instantly.
Inside the Summation Of Series Calculator
Under the hood, this calculator applies aₙ = a + (n−1)d; Sₙ = n(a + aₙ)÷2 = n÷2 × (2a + (n−1)d), so the summation of series calculator result you see is genuine math, not a lookup table.
The reference table below covers the most common summation of series calculator cases at a glance, the methodology section breaks the calculation into verifiable steps, and the FAQ tackles the edge cases.
Quick reference
| Series | Sum |
|---|---|
| 1+2+…+100 (a=1, d=1, n=100) | 5,050 |
| 2+5+8+… (a=2, d=3, n=10) | 155 |
| 5+10+…+50 (a=5, d=5, n=10) | 275 |
| Odd numbers 1+3+… (n=10) | 100 |
functions Shows the working, not just the answer
For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.
calculate Accurate to the spec
Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.
school Free for classroom use
Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.
tips_and_updates Pair with the spoke articles
Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.
Interpretation guide
| Quantity | Meaning |
|---|---|
| aₙ (last term) | a + (n−1)d — where the series ends |
| Average term | (a + aₙ)÷2 — the series’ midpoint |
| Sum | n × average term |
Formula & methodology
Formula: aₙ = a + (n−1)d; Sₙ = n(a + aₙ)÷2 = n÷2 × (2a + (n−1)d)
- Enter the first term a, the common difference d and the number of terms n.
- The last term is aₙ = a + (n−1)d.
- The sum uses Gauss’s pairing trick: S = n × (a + aₙ) ÷ 2.
Example: a = 2, d = 3, n = 10 → last term 29, sum = 10 × (2+29)÷2 = 155.