Find The 13th Term of The Following Geometric Sequence Calculator

Finding the nth term of a geometric sequence is a common math problem. This calculator helps you determine the 13th term of any geometric sequence by inputting the first term and common ratio.

How to Use This Calculator

To find the 13th term of a geometric sequence:

Enter the first term (a₁) of the sequence
Enter the common ratio (r) between terms
Click "Calculate" to see the 13th term

The calculator will display the result and show a chart of the sequence terms.

The Formula Explained

The nth term of a geometric sequence can be found using the formula:

aₙ = a₁ × r^(n-1)

Where:

aₙ = nth term
a₁ = first term
r = common ratio
n = term number

For the 13th term (n=13), the formula becomes:

a₁₃ = a₁ × r^(12)

This formula works for any geometric sequence where each term is found by multiplying the previous term by the common ratio.

Worked Example

Let's find the 13th term of a sequence where:

First term (a₁) = 5
Common ratio (r) = 2

Using the formula:

a₁₃ = 5 × 2^(12)

a₁₃ = 5 × 4096

a₁₃ = 20480

The 13th term of this sequence is 20,480.

Frequently Asked Questions

What is a geometric sequence?

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio.

How do I find the common ratio?

The common ratio can be found by dividing any term by its preceding term. For example, if the second term is 8 and the first term is 2, the common ratio is 8/2 = 4.

What if the common ratio is negative?

The formula still works with negative common ratios. The terms will alternate in sign, but the absolute values will follow the geometric pattern.