# Question 7

The first three terms of a geometric sequence are as follows.
10,30,90

The next term 90 * 3 = 270

Does that help?

## To find the common ratio, we can divide any term by its preceding term.

30 ÷ 10 = 3
90 ÷ 30 = 3

Since both divisions give us the same result, we can conclude that the common ratio is 3.

To find the fourth term, we can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)

Where:
an = nth term
a1 = first term
r = common ratio
n = position of the term

In this case, a1 = 10, r = 3, and n = 4.

a4 = 10 * 3^(4-1)
= 10 * 3^3
= 10 * 27
= 270

Therefore, the fourth term of the geometric sequence is 270.

## To determine the common ratio of this geometric sequence, we need to divide any term by its preceding term. Let's calculate the common ratio using the first two terms.

Divide the second term by the first term:
30 / 10 = 3

We found that the common ratio between consecutive terms in this sequence is 3.

With the common ratio, we can then determine the next term(s) in the sequence. To find the fourth term, we can multiply the third term by the common ratio:

90 * 3 = 270

Therefore, the fourth term in this geometric sequence is 270.

-3,15,-75