Question

Write your own example of a geometric sequence. Identify your common ratio and give at least 4 terms.

In a geometric sequence, what is the common ratio?

a) The sum of the first and last terms
b) The difference between the first and second terms
c) The product of any two consecutive terms
d) The average of all the terms

Answer 1

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the preceding term by a fixed, non-zero number called the common ratio. The common ratio is found by dividing any term by its preceding term.

Step-by-step explanation:

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the preceding term by a fixed, non-zero number called the common ratio. For example, consider the sequence: 2, 6, 18, 54. The common ratio is 3 since each term is obtained by multiplying the previous term by 3.

Let's identify the common ratio of this example:

• First term: 2
• Second term: 6
• Third term: 18
• Fourth term: 54

To find the common ratio, we can divide any term by its preceding term. Dividing the second term (6) by the first term (2) gives us a result of 3. This means the common ratio is 3.