Certified calculator · Version 1

Sequence Calculator

Find the nth term, finite sum and initial terms of an arithmetic progression from its first term and common difference.

First term (a₁)Common difference (d)Term number (n)

Nth term19

Sum of first n terms100

Term preview1, 3, 5, 7, 9, 11, 13, 15, 17, 19

Trend

Included with Free

611

713

815

917

1019

Visual scale

Accessible data view

CalcuMint Pro

Advanced Analysis

Compare plans

Advanced chartsExplore the result across time and assumptions.

Scenario comparisonCompare multiple assumptions side by side.

Sensitivity analysisSee which assumptions change the outcome most.

Goal SolverSolve backwards from the outcome you want.

Result methodology

The certified arithmetic-sequence engine calculates the nth term and finite sum, while the Free trend preview is generated from the same progression.

Solution steps

aₙ = 1 + (10-1)×2 = 19
Sₙ = 10(1+19)/2 = 100

How this calculator works

For an arithmetic sequence, aₙ=a₁+(n−1)d and Sₙ=n(a₁+aₙ)/2.

Formula

aₙ=a₁+(n-1)d; Sₙ=n(a₁+aₙ)/2

Computes an arithmetic sequence term and finite sum.

Worked example

First 10 odd numbers is a verified test case used by the calculation engine.

Assumptions and limitations

This certified version covers arithmetic sequences.
n is an integer from 1 through 1000; the preview shows at most 20 terms.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint.

CalcuMint deterministic sequence engine — Standard arithmetic progression identities.

Frequently asked questions

Which sequence type is supported?

This version calculates arithmetic sequences with a constant common difference.

Does it calculate the sum?

Yes. It returns the nth term and the sum of the first n terms.