Find N in Arithmetic Sequence Calculator

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This calculator helps you find the nth term in an arithmetic sequence using the first term, common difference, and the position n.

What is an Arithmetic Sequence?

An arithmetic sequence is a sequence of numbers where the difference between each consecutive term is constant. This difference is known as the common difference, often denoted by 'd'. The sequence can be written as:

a, a + d, a + 2d, a + 3d, ...

Where:

a is the first term
d is the common difference

For example, the sequence 2, 5, 8, 11, 14 is an arithmetic sequence where a = 2 and d = 3.

Formula for Finding n

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

aₙ = a + (n - 1) × d

Where:

aₙ is the nth term
a 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 if you know the first term, common difference, and the position of the term you want to find.

How to Use the Calculator

Enter the first term (a) of the arithmetic sequence
Enter the common difference (d) between terms
Enter the term number (n) you want to find
Click the "Calculate" button
View the result showing the nth term

The calculator will display the nth term of the sequence based on the values you provide. You can also see a visualization of the sequence.

Examples

Example 1

Given an arithmetic sequence with first term a = 3 and common difference d = 2, find the 5th term.

Using the formula:

a₅ = 3 + (5 - 1) × 2 = 3 + 8 = 11

The 5th term is 11.

Example 2

Given an arithmetic sequence with first term a = 10 and common difference d = -3, find the 4th term.

Using the formula:

a₄ = 10 + (4 - 1) × (-3) = 10 - 9 = 1

The 4th term is 1.

Example 3

Given an arithmetic sequence with first term a = 7 and common difference d = 5, find the 7th term.

Using the formula:

a₇ = 7 + (7 - 1) × 5 = 7 + 30 = 37

The 7th term is 37.

FAQ

What is the difference between arithmetic and geometric sequences?: An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio between terms.
Can the common difference be negative?: Yes, the common difference can be negative, which means the sequence decreases as it progresses.
What if I enter a non-integer value for n?: The calculator will still work, but the result may not correspond to a term in the sequence. Typically, n is a positive integer.
How can I verify the result from the calculator?: You can manually apply the formula aₙ = a + (n - 1) × d with the values you entered to verify the result.
Is there a limit to how large n can be?: The calculator can handle very large values of n, but extremely large numbers may cause display or calculation issues.