Find The 10th Term of The Following Geometric Sequence Calculator

Finding the 10th term of a geometric sequence is a common math problem that appears in algebra, finance, and other fields. This calculator provides an easy way to determine the 10th term of any geometric sequence you encounter.

How to Use This Calculator

To find the 10th term of a geometric sequence, you need to know the first term (a₁) and the common ratio (r). Here's how to use our calculator:

Enter the first term of your sequence in the "First term (a₁)" field.
Enter the common ratio in the "Common ratio (r)" field.
Click the "Calculate" button to see the result.
The calculator will display the 10th term of your sequence.

If you need to find a different term (not the 10th), you can modify the formula shown below to use your desired term number.

The Formula Explained

The general formula for finding the nth term of a geometric sequence is:

aₙ = a₁ × r^(n-1)

Where:

aₙ = the nth term you want to find
a₁ = the first term of the sequence
r = the common ratio between terms
n = the term number you want to find

For this calculator, we're specifically finding the 10th term (n=10), so the formula becomes:

a₁₀ = a₁ × r^(9)

This means we multiply the first term by the common ratio raised to the power of 9 (since we're finding the 10th term, which is 9 steps from the first term).

Worked Example

Let's work through an example to see how this calculator works. Suppose we have a geometric sequence where:

First term (a₁) = 3
Common ratio (r) = 2

We want to find the 10th term (a₁₀). Using the formula:

a₁₀ = 3 × 2^(9)

a₁₀ = 3 × 512

a₁₀ = 1536

So, the 10th term of this sequence is 1536. You can verify this by entering these values into our calculator.

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 the previous term. For example, if the sequence is 2, 6, 18, 54, the common ratio is 6/2 = 3.

Can the common ratio be negative?

Yes, the common ratio can be negative. This creates an alternating sequence where terms switch between positive and negative values.

What if the common ratio is 1?

If the common ratio is 1, the sequence becomes a constant sequence where all terms are equal to the first term.