Arithmetic Sequence Calculator

What is an Arithmetic Sequence?

Imagine you're climbing a staircase. Each step you take is the same height as the one before. That's just like an arithmetic sequence! It's a list of numbers where the difference between each number and the next is always the same. We call this difference the "common difference".

How to Calculate an Arithmetic Sequence

To find any term in an arithmetic sequence, we start with the first term and add the common difference as many times as needed. It's like taking steps up that staircase!

Formula

The formula for the nth term of an arithmetic sequence is:

\[ a_n = a_1 + (n - 1)d \]

Where:

• \(a_n\) is the nth term of the sequence
• \(a_1\) is the first term
• \(n\) is the position of the term we're looking for
• \(d\) is the common difference between terms

Calculation Steps

1. Identify the first term (\(a_1\))
2. Find the common difference (\(d\)) by subtracting any term from the next term
3. Decide which term you want to find (\(n\))
4. Plug these values into the formula: \(a_n = a_1 + (n - 1)d\)
5. Solve the equation to find your answer

Example

Let's look at the sequence: 3, 7, 11, 15, 19, ...

• First term (\(a_1\)) is 3
• Common difference (\(d\)) is 4 (7 - 3 = 4, 11 - 7 = 4, etc.)
• Let's find the 6th term (\(n = 6\))

Using our formula:

\(a_6 = 3 + (6 - 1)4 = 3 + 20 = 23\)

So, the 6th term is 23!

Visual Representation