Arithmetic Sequence Calculator

Q: How do I find the nth term of an arithmetic sequence?

Use the formula: a_n = a_1 + (n - 1) * d, where a_1 is the first term and d is the common difference.

Calculator

First Term (a₁) *

Common Difference (d) *

Term Number (n) *

Results

Nth Term (a_n) N/A

Data Source and Methodology

All calculations are rigorously based on standard arithmetic sequence formulas. For detailed information, please consult algebraic textbooks or educational websites.

The Formula Explained

To find the nth term of an arithmetic sequence, use the formula:

a_n = a₁ + (n - 1) × d

Glossary of Terms

First Term (a₁): The initial number in the sequence.
Common Difference (d): The consistent difference between consecutive terms.
Term Number (n): The position of the term in the sequence.
Nth Term (a_n): The term at position 'n' in the sequence.

How It Works: A Step-by-Step Example

Consider a sequence starting at 3, with a common difference of 5, and you want to find the 10th term:

First Term (a₁) = 3
Common Difference (d) = 5
Term Number (n) = 10
Calculation: a₁₀ = 3 + (10 - 1) × 5 = 48

Frequently Asked Questions (FAQ)

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

How do I find the nth term of an arithmetic sequence?

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

Can an arithmetic sequence have a negative common difference?

Yes, a negative common difference means the sequence decreases.

What is the sum of an arithmetic sequence?

The sum of the first n terms of an arithmetic sequence can be found using the formula: S_n = n/2 × (2a₁ + (n - 1) × d).

Are all sequences arithmetic?

No, sequences can follow different patterns and not all have a constant difference.

Tool developed by Ugo Candido. Content reviewed by the CalcDomain Expert Team. Last reviewed for accuracy on: October 20, 2023.