## The value of the fourth term in a geometric sequence

### What is a geometric sequence?

In mathematics, a geometric sequence, also known as a geometric progression, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54… is a geometric sequence with a common ratio 3. Each successive term is found by multiplying the previous term by 3.

The fourth term in a geometric sequence can be found by multiplying the common ratio by itself three times and then multiplying this result by the first term. For example, in the sequence 2, 6, 18, 54… , the fourth term can be found by multiplying 3 by itself three times (3 x 3 x 3 = 27) and then multiplying this result by the first term (27 x 2 = 54).

### What is the fourth term in a geometric sequence?

The fourth term in a geometric sequence is found by multiplying the common ratio by the third term. In this instance, the common ratio is 12 and the third term is 30, so the fourth term would be 360.

### What is the value of the fourth term in a geometric sequence for which a1=30 and r=12?

The fourth term in a geometric sequence is found by multiplying the common ratio by the third term. In this case, the common ratio is 12 and the third term is 30, so the fourth term would be 30 multiplied by 12, or 360.

## How to calculate the value of the fourth term in a geometric sequence

In a geometric sequence, each term after the first is equal to the previous term multiplied by a common ratio, r. The fourth term in a geometric sequence can be calculated by multiplying the previous three terms together and then dividing by the common ratio.

### What is the formula for calculating the fourth term in a geometric sequence?

There is a formula for calculating the fourth term in a geometric sequence. The formula is:

a4 = a1 * r^3

Where:

a1 = the first term in the sequence

r = the common ratio between terms

a4 = the fourth term in the sequence

Applying this formula to the given sequence, we get:

a4 = 30 * 12^3

a4 = 30 * 1728

a4 = 51840

### How to use the formula to calculate the fourth term in a geometric sequence for which a1=30 and r=12

Geometric sequences have a common ratio between successive terms. This means that the after the first term, each term is equal to the previous term multiplied by some number, r. In this lesson, we will look at how to calculate the fourth term in a geometric sequence when we are given the first term and the common ratio.

First, let’s review what we know about geometric sequences. A geometric sequence is a sequence of numbers where each term after the first is equal to the previous term multiplied by some number, r. We can represent a geometric sequence using notation as follows:

a_n=a_1r^{n-1}

In this equation, a_n represents any arbitrary term in our sequence, a_1 represents the first term in our sequence, and r represents our common ratio. n represents the position of our arbitrary term in terms of counting from the first term– thus, n-1 would represent everything counting up to but not including our arbitrary term.

Now let’s apply this equation to calculate the fourth term in our geometric sequence when we are given that:

```
a_1=30
r=12
```

When we plug these values into our equation for a_n, we get:

a_4=30\cdot 12^{4-1}

a_4=30\cdot 12^{3}

a_4=3600

## The answer

### The value of the fourth term in a geometric sequence for which a1=30 and r=12 is 2160

The value of the fourth term in a geometric sequence for which a1=30 and r=12 is 2160.