FoodyShagor - Free Online Tools and Utilities

Sequence Type: Arithmetic Sequence Geometric Sequence

First Term (a₁):

Common Difference (d):

Term Position (n):

Result:

Enter values to calculate

Sequence Calculator Tool

Sequence Calculator: Find the Nth Term

Easily calculate any term in arithmetic or geometric sequences with our powerful online tool. Perfect for students, teachers, and math enthusiasts.

How to Use the Sequence Calculator

Our sequence calculator helps you find any term in arithmetic or geometric sequences:

1. Select the sequence type (arithmetic or geometric)
2. Enter the first term of the sequence
3. Enter the common difference (for arithmetic) or common ratio (for geometric)
4. Specify which term position you want to find
5. Click "Calculate Nth Term" to get your result

Arithmetic Sequence Formula

The nth term of an arithmetic sequence is calculated using the formula:

aₙ = a₁ + (n - 1) × d

Where:

aₙ = nth term

a₁ = first term

n = term position

d = common difference

Geometric Sequence Formula

The nth term of a geometric sequence is calculated using the formula:

aₙ = a₁ × r⁽ⁿ⁻¹⁾

Where:

aₙ = nth term

a₁ = first term

n = term position

r = common ratio

Frequently Asked Questions

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This difference is called the "common difference." For example: 2, 5, 8, 11, 14... is an arithmetic sequence with a common difference of 3.

What is a geometric sequence?

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the "common ratio." For example: 3, 6, 12, 24, 48... is a geometric sequence with a common ratio of 2.

What if I have a negative common ratio?

The calculator works perfectly with negative common ratios. For example, a geometric sequence with first term 4 and common ratio -2 would be: 4, -8, 16, -32, 64...