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Arithmetic Sequence Calculator

Calculate nth terms, common differences, sums, and arithmetic sequences instantly.

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Input Values

Enter your known sequence values to calculate.

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Enter your sequence values and click Calculate to see the result, formulas, and visual preview.

Calculation Complete

Nth Term (aₙ)

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Sum (Sₙ)

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Step-by-Step Solution

1. Finding the Nth Term (aₙ)

Given:
a₁ = , d = , n =
Formula:
aₙ = a₁ + (n - 1)d
Substitute:
a = + ( - 1)()
Calculate:
a = + ()
Answer:
a =

2. Finding the Sum (Sₙ)

Formula:
Sₙ = (n/2) × (a₁ + aₙ)
Substitute:
S = (/2) × ( + )
Answer:
S =

Sequence Preview

Visualization

Sequence Table (First 10)

Term (n) Value (aₙ) Sum so far (Sₙ)

What Is an Arithmetic Sequence?

An arithmetic sequence (or progression) is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant is known as the common difference (d).

Key Formulas

Nth Term (aₙ)

aₙ = a₁ + (n - 1)d

Used to find any term in the sequence.

Sum of First n Terms (Sₙ)

Sₙ = n/2 × [2a₁ + (n - 1)d]

Alternative: Sₙ = n/2 × (a₁ + aₙ)

Used to find the total sum of the sequence up to n terms.

Examples

Example: Finding the 10th term

Given: Sequence is 3, 7, 11, 15...

  • First term (a₁) = 3
  • Common difference (d) = 7 - 3 = 4
  • Number of terms (n) = 10

Calculation: a₁₀ = 3 + (10 - 1)4 = 3 + (9)4 = 3 + 36 = 39

Frequently Asked Questions

Can the common difference be negative?
Yes. If the sequence is decreasing (e.g., 10, 8, 6, 4), the common difference is negative (in this case, -2).
Can I use decimal numbers?
Absolutely. Arithmetic sequences can consist of fractions, decimals, or negative numbers.
What is the difference between a sequence and a series?
A sequence is the list of numbers (e.g., 2, 4, 6), whereas a series is the sum of those numbers (e.g., 2 + 4 + 6 = 12).
Is this Arithmetic Sequence Calculator free?
Yes, this online calculator is completely free to use without any registration required.

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