Find N 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 of an arithmetic sequence using the first term and 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. The constant difference is called the common difference.

Examples of arithmetic sequences include:

2, 5, 8, 11, 14 (common difference of 3)
10, 7, 4, 1, -2 (common difference of -3)
1, 1, 1, 1, 1 (common difference of 0)

Arithmetic sequences are fundamental in mathematics and have applications in various fields such as 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 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 and the common difference.

How to Use the Calculator

Using the 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

The calculator will display the nth term of the sequence and provide an explanation of the calculation.

Note: The term number (n) must be a positive integer. The calculator will validate your input to ensure it's a valid number.

Examples of Arithmetic Sequences

Let's look at a few examples to see how the calculator works.

Example 1

Given the arithmetic sequence: 3, 7, 11, 15, 19...

First term (a₁) = 3
Common difference (d) = 4
Find the 5th term (n = 5)

Using the formula:

a₅ = 3 + (5 - 1) × 4 = 3 + 16 = 19

The 5th term is 19, which matches the sequence.

Example 2

Given the arithmetic sequence: 10, 6, 2, -2, -6...

First term (a₁) = 10
Common difference (d) = -4
Find the 6th term (n = 6)

Using the formula:

a₆ = 10 + (6 - 1) × (-4) = 10 - 20 = -10

The 6th term is -10.

Frequently Asked Questions

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.

Can the common difference be negative?

Yes, the common difference can be negative, which results in a decreasing arithmetic sequence.

What if the term number is not an integer?

The term number must be a positive integer. The calculator will validate your input to ensure it's a valid number.

How can I find the sum of the first n terms of an arithmetic sequence?

You can use the sum formula: Sₙ = n/2 × (2a₁ + (n - 1)d). There's a separate calculator for this purpose.