Find N Term Arithmetic Sequence Calculator

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This calculator helps you find any term in an arithmetic sequence when you know the first term and the common difference.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers where each term after the first is obtained by adding a constant difference to the preceding term. This constant difference is called the common difference.

For example, the sequence 2, 5, 8, 11, 14 is an arithmetic sequence where the first term (a₁) is 2 and the common difference (d) is 3.

Arithmetic sequences are fundamental in mathematics and appear in many real-world applications, including finance, physics, and computer science.

Formula for finding the nth term

The nth term of an arithmetic sequence can be found using the following formula:

aₙ = a₁ + (n - 1) × d

Where:

aₙ = nth term
a₁ = first term
d = common difference
n = term number

This formula allows you to calculate any term in the sequence by knowing the first term and the common difference.

How to use the calculator

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 find the nth term.
Review the result and chart showing the sequence.

All calculations are done instantly in your browser with no data sent to servers.

Examples of arithmetic sequences

Sequence	First Term (a₁)	Common Difference (d)	5th Term (a₅)
3, 7, 11, 15, 19, ...	3	4	19
10, 6, 2, -2, -6, ...	10	-4	-6
0, 0.5, 1, 1.5, 2, ...	0	0.5	2

These examples demonstrate how the same formula can be applied to different arithmetic sequences.

FAQ

What is the difference between an arithmetic sequence and a geometric sequence?

An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio between terms. For example, 2, 4, 8, 16 is a geometric sequence with a common ratio of 2.

Can the common difference be negative?

Yes, the common difference can be negative, which results in a decreasing arithmetic sequence. For example, 10, 6, 2, -2, -6 has a common difference of -4.

What if I only know two terms in the sequence?

If you know two terms, you can find the common difference by subtracting the first term from the second term. Then use the formula to find other terms.