When you study geometry in Year 9 Math, it's important to learn how to find the nth term in a geometric sequence.

So, what is a geometric sequence?

A geometric sequence is a list of numbers where each number after the first one is found by multiplying the previous number by a fixed number. This fixed number is called the common ratio, which we write as $r$.

The Formula

To find the nth term of a geometric sequence, you can use this formula:

$$a_n = a_1 \times r^{(n-1)}$$

Here’s what the symbols mean:

• $a_n$ is the term you want to find.
• $a_1$ is the first term in the sequence.
• $r$ is the common ratio.
• $n$ is the position of the term in the sequence.

Example

Let’s check out a simple example.

Imagine we have a geometric sequence where:

• The first term ($a_1$) is 3.
• The common ratio ($r$) is 2.

To find the 5th term ($a_5$), we just plug in the numbers into the formula:

$$a_5 = 3 \times 2^{(5-1)}$$ $$= 3 \times 2^4$$ $$= 3 \times 16$$ $$= 48$$

Conclusion

Now you know that the 5th term of this sequence is 48!

By understanding how to use this formula, you can feel more confident when solving problems with geometric sequences.

Try practicing with different numbers to get better at it!