Arithmetic Sequence Calculator - Calculator See


Arithmetic Sequence Calculator

Calculate the nth term, common difference (d), and sum of arithmetic series.

Calculator Inputs

Starting term.
Step size added.
Target term position.

Calculated Results

N-th Term Value (a_n)
47 (at n = 10)
Sum of First n Terms (S_n) 245
Common Difference (d) 5
Sequence Formula a_n = 2 + (n-1)*5
Values calculate live as you adjust inputs.

About Arithmetic Sequence Calculator

Evaluates sequences where each successive number is obtained by adding a fixed constant common difference d.

What is Arithmetic Sequence Calculator?

Evaluates sequences where each successive number is obtained by adding a fixed constant common difference d.

How to Use This Calculator

  1. Enter first term a1 and common difference d.
  2. Enter target position n.
  3. View term value and sum of terms.

The Mathematical Formula & Variables

an = a1 + (n - 1) * d; Sn = (n / 2) * (a1 + an)

Step-by-Step Worked Example

Scenario: a1 = 2, d = 5, n = 10.

  1. a10 = 2 + (10 - 1) * 5 = 2 + 45 = 47.
  2. Sum S10 = (10 / 2) * (2 + 47) = 5 * 49 = 245.

Result: 47

Frequently Asked Questions

Who discovered the formula for the sum of an arithmetic series?

Carl Friedrich Gauss famously discovered the shortcut as a young schoolchild by pairing numbers from opposite ends of the series.