N Th Term Calculator

An nth term calculator helps you find any term in an arithmetic sequence. Whether you're studying math, analyzing data, or solving real-world problems, this tool provides quick and accurate results.

What is the nth term?

The nth term refers to any term in 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 (d).

The first term of the sequence is often denoted as a₁, and the nth term is denoted as aₙ. The position of the term in the sequence is given by the term number (n).

Formula

The formula to find the nth term of an arithmetic sequence is:

aₙ = a₁ + (n - 1) × d

Where:

aₙ is the nth term
a₁ is the first term
d is the common difference
n is the term number

This formula allows you to calculate any term in the sequence once you know the first term, common difference, and the term number.

How to use the calculator

Using the nth term calculator is simple:

Enter the first term (a₁) of the arithmetic sequence.
Enter the common difference (d) between terms.
Enter the term number (n) you want to find.
Click the "Calculate" button to get the nth term.

The calculator will display the result and show you the calculation steps.

Examples

Let's look at a few examples to understand how the nth term calculator works.

Example 1

Consider an arithmetic sequence where the first term (a₁) is 5 and the common difference (d) is 3. Find the 10th term (a₁₀).

a₁₀ = 5 + (10 - 1) × 3 = 5 + 27 = 32

The 10th term of the sequence is 32.

Example 2

For a sequence with a₁ = 10 and d = -2, find the 7th term (a₇).

a₇ = 10 + (7 - 1) × (-2) = 10 + (-12) = -2

The 7th term of the sequence is -2.

FAQ

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.
How do I find the nth term of an arithmetic sequence?: You can use the formula aₙ = a₁ + (n - 1) × d, where aₙ is the nth term, a₁ is the first term, d is the common difference, and n is the term number.
Can the common difference be negative?: Yes, the common difference can be negative, which means the sequence decreases by a constant amount with each term.
What if I don't know the first term?: If you don't know the first term, you can use other information about the sequence, such as two known terms, to find the common difference and then determine the first term.
Is the nth term calculator accurate?: Yes, the nth term calculator uses the standard arithmetic sequence formula and provides accurate results based on the inputs you provide.