Mathematics, Statistics & Geometry

Arithmetic Sequence Calculator

Calculate any term and the sum of an arithmetic sequence instantly. Find the common difference, n-th term, and partial sum step by step.

Value of Term n=10
19
Sum of First 10 Terms100
Common Difference (d)2
First Term (a₁)1
Calculation StepsArithmetic Sequence: aₙ = a₁ + (n - 1)d a₁ = 1, d = 2, n = 10 aₙ = 1 + (10 - 1) * 2 = 19.000000 Sum Sₙ = (n/2)(a₁ + aₙ) Sₙ = (10/2)(1 + 19.000000) = 100.000000

Calculated locally in your browser. Fast, secure, and private.

Master Linear Patterns

The Arithmetic Sequence calculator is a powerful tool for analyzing linear number patterns. Whether you are calculating future savings, predicting population growth, or solving algebraic progressions, this calculator provides the exact value of any term and the total sum of the sequence.

an=a1+(n−1)d,Sn=n2(a1+an)\begin{aligned} a_n = a_1 + (n-1)d, \quad S_n = \frac{n}{2}(a_1 + a_n) \end{aligned}

Where:
ana_n=
The value of the term at position n
a1a_1=
The starting value of the sequence
d=
The constant value added to each term
n=
The position of the term in the sequence
SnS_n=
The sum of the first n terms

Key Components of the Sequence

  1. First Term (a₁): Where the sequence begins.
  2. Common Difference (d): The amount added (or subtracted) at each step.
  3. Term Number (n): The specific position you are interested in (e.g., the 100th term).
  4. n-th Term (aₙ): The value of the number at position n.

Arithmetic Progression in Real Life

  • Financial Planning: Calculating simple interest or flat-rate savings contributions.
  • Physics: Analyzing motion with constant acceleration.
  • Computer Science: Managing loop iterations and linear data structures.
  • Music: Analyzing scales and rhythmic patterns based on equal intervals.

How to use this calculator

Enter your starting value and the difference between steps. Our tool will instantly generate the value for your target term and the cumulative sum of all terms leading up to it, complete with a full step-by-step mathematical breakdown.

Frequently Asked Questions

An arithmetic sequence is a list of numbers where the difference between any two consecutive terms is constant. For example: 2, 5, 8, 11... (difference is 3).

Use the formula aₙ = a₁ + (n-1)d, where a₁ is the first term, n is the position, and d is the common difference.

Use the formula Sₙ = (n/2) × (a₁ + aₙ). This is often called the arithmetic series formula.

Yes. If the common difference is negative, the sequence is decreasing (e.g., 10, 7, 4, 1...).

In an arithmetic sequence, you add a constant difference. In a geometric sequence, you multiply by a constant ratio.

Related Calculators in Mathematics, Statistics & Geometry

Angle Between Vectors Calculator

Try It Now

ANOVA Calculator

Try It Now

Antilog Calculator

Try It Now

Arc Length of Curve Calculator

Try It Now

Area of Annulus Calculator

Try It Now

Area of Circle Calculator

Try It Now