Find The 55th Term of The Following 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 55th term of any arithmetic sequence when you know the first term and the common difference.

Introduction

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 general form of an arithmetic sequence is:

a₁, a₁ + d, a₁ + 2d, a₁ + 3d, ..., a₁ + (n-1)d

Where:

a₁ is the first term
d is the common difference between terms
n is the term number

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

Arithmetic Sequence Formula

aₙ = a₁ + (n - 1) × d

This calculator applies this formula to find the 55th term of any arithmetic sequence you provide.

How to Use the Calculator

Enter the first term (a₁) of your arithmetic sequence in the first input field.
Enter the common difference (d) between terms in the second input field.
Click the "Calculate" button to find the 55th term.
The result will appear in the result box below the calculator.
You can reset the calculator by clicking the "Reset" button.

Tip

For best results, ensure your inputs are accurate. The calculator will work with both positive and negative numbers.

Formula Explained

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

Arithmetic Sequence Formula

aₙ = a₁ + (n - 1) × d

Where:

aₙ is the nth term you want to find
a₁ is the first term of the sequence
n is the term number (in this case, 55)
d is the common difference between terms

This formula works by starting with the first term and then adding the common difference multiplied by (n - 1) to get to the nth term.

Worked Example

Let's find the 55th term of an arithmetic sequence where the first term (a₁) is 3 and the common difference (d) is 2.

Using the formula:

Calculation

a₅₅ = 3 + (55 - 1) × 2

a₅₅ = 3 + 54 × 2

a₅₅ = 3 + 108

a₅₅ = 111

So, the 55th term of this arithmetic sequence is 111.

Frequently Asked Questions

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. Each term after the first is found by adding a fixed number 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. This would result in a decreasing arithmetic sequence where each term is smaller than the previous one.

What if I don't know the first term?

You would need at least one term and the common difference to use the formula. If you have another term from the sequence, you can rearrange the formula to solve for a₁.