Sequence Sum Calculator

Work out sequence sum instantly with clear inputs, formula shown and shareable results.

About Sequence Sum Calculator

An arithmetic series sums to n/2 times the sum of the first and last terms. A geometric series sums to a(rⁿ − 1)/(r − 1), reducing to n·a when the ratio is exactly 1.

Formulas

Arithmetic sum

Sₙ = n/2 · (2a + (n − 1)d) = n/2 · (first + last)

Geometric sum

Sₙ = a(rⁿ − 1) / (r − 1)

Worked example

With the default values below, Sequence Sum Calculator returns Sum of the terms of 120.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

First term: 3
Common difference or ratio: 2
Number of termsaccepts 1–1,000,000: 10
Sequence typeone of Arithmetic, Geometric: Arithmetic

Results

Sum of the terms: 120.00000000
Last term: 21.00000000
Average term: 12.00000000
Formula used: Sₙ = n/2 (2a + (n-1)d)

Step by step

1Values used
2Arithmetic sum
3Geometric sum
4Sum of the terms= 120.00000000
5Last term= 21.00000000
6Average term= 12.00000000
7Formula used= Sₙ = n/2 (2a + (n-1)d)

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Sum of 3, 5, 7, … for 10 terms?

10/2 × (6 + 18) = 5 × 24 = 120.

Why does the arithmetic formula use the average?

Because evenly spaced terms have a mean equal to the midpoint of the first and last, so the sum is n times that midpoint.