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How to Calculate Arithmetic Sequence

What is Arithmetic Sequence?

An arithmetic sequence is a list of numbers where consecutive terms differ by a constant value called the common difference (d). Examples include: 2, 5, 8, 11... (d=3) or 10, 7, 4, 1... (d=−3).

Formula

nth term: aₙ = a₁ + (n−1) × d

Step-by-Step Guide

  1. 1nth term: aₙ = a₁ + (n−1) × d
  2. 2Sum of n terms: Sₙ = n/2 × (2a₁ + (n−1)d) = n/2 × (first + last)
  3. 3If you know any two terms and their positions, you can find d

Worked Examples

Input
First term 3, difference 4, find 10th term
Result
a₁₀ = 3 + 9×4 = 39
3, 7, 11, 15, 19, 23, 27, 31, 35, 39
Input
Sum of first 100 natural numbers
Result
5,050
a₁=1, d=1, S₁₀₀ = 100/2 × (1+100) = 5,050

Frequently Asked Questions

What is Arithmetic Sequence?

An arithmetic sequence is a list of numbers where consecutive terms differ by a constant value called the common difference (d). Examples include: 2, 5, 8, 11

How accurate is the Arithmetic Sequence calculator?

The calculator uses the standard published formula for arithmetic sequence. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Arithmetic Sequence calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Arithmetic Sequence calculator use?

The core formula is: nth term: aₙ = a₁ + (n−1) × d. Each step in the calculation is shown so you can verify the result manually.

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