What Is the Common Ratio of the Geometric Sequence Below?

The common ratio of a geometric sequence is the number that is multiplied by each term to produce the next term. In the sequence below, the common ratio is 3.

1, 3, 9, 27, 81, ...

A geometric sequence is a sequence of numbers where each term is the previous term multiplied by a common ratio. A common ratio is a number that is multiplied by each term to produce the next term. In the sequence below, the common ratio is 3.

The first term in the sequence is 1 and the second term is 3. To find the third term, we multiply the common ratio, 3, by the second term, 3, to get 9. To find the fourth term, we multiply the common ratio by the third term, 9, to get 27. And so on.

So, the common ratio is responsible for the sequence "growing" or "shrinking". If the common ratio is greater than 1, the sequence will "grow" or get larger with each term. If the common ratio is between 0 and 1, the sequence will "shrink" or get smaller with each term.

In the sequence below, the common ratio is 3. Since 3 is greater than 1, the sequence will "grow" or get larger with each term.

1, 3, 9, 27, 81, ...

The common ratio is an important concept in mathematics, especially when it comes to geometric sequences. So, it's important to be able to identify the common ratio in a given sequence.

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The number 3 is a strong and powerful number. It represents the Trinity, which is the Father, Son, and Holy Spirit. The number 9 is a very important number in the Bible. It represents the nine fruits of the Spirit, which are love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, and self-control. The number 27 is a important number too. It represents the 27 books of the New Testament.

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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 1, 3, 9, 27... is a geometric sequence with common ratio 3, because each term can be obtained by multiplying the previous one by 3.

The common ratio of a geometric sequence is the number by which each term is multiplied to get the next term. In the example above, the common ratio is 3.

The common ratio of a geometric sequence can be found by dividing any term by the preceding term. For example, the common ratio of the sequence 1, 3, 9, 27... can be found by dividing 3 by 1, 9 by 3, or 27 by 9, which all give 3.

The common ratio of a geometric sequence is also the exponent to which the first term is raised to get the second term. In the example above, the common ratio is 3, because the second term (3) can be obtained by raising the first term (1) to the power of 3.

The terms of a geometric sequence with a common ratio of 1 are called arithmetic sequence.

For more insights, see: Geometric Series

The next term in the sequence if the common ratio is 3 would be 9. This is because each subsequent term in the sequence is equal to the previous term multiplied by the common ratio. Therefore, since 3 is the common ratio, the next term would be 3 times the previous term, which is 3 times 3, or 9.

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The next term in the sequence if the common ratio is 9 is 81.

In mathematics, a sequence is a list of elements (usually numbers) that are connected in some way. In this case, the common ratio is the number that each term in the sequence is multiplied by to get the next term. So, if the common ratio is 27, the next term in the sequence would be 27 times the current term. For example, if the current term is 2, then the next term would be 2 x 27, or 54.

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In mathematics, a sequence is a string of numbers that follow a particular pattern. The previous term in a sequence is the term that comes before the current term. In other words, it is the term that is one step behind the current term. If the common ratio is 3, then the previous term in the sequence is 9.

The previous term in the sequence is 36. The common ratio is 9.

There is no definitive answer to this question since it depends on what the initial term of the sequence is. However, if we assume that the initial term is 1, then the previous term in the sequence would be 1/27. This is because each successive term in the sequence is obtained by multiplying the previous term by the common ratio, which in this case is 27. Therefore, the second term in the sequence would be 1*27 = 27, the third term would be 27*27 = 729, and so on.

In mathematics, a sequence is an ordered set of objects in which repetitions are allowed. A sequence can be finite, meaning that it has a definite end, or infinite, meaning that it does not end. A sequence can also be specified by a function, called its generating function, which produces the objects in the sequence.

The sum of the first four terms of a sequence is called the fourth partial sum. If the common ratio is 3, then the fourth partial sum is 3 + 9 + 27 + 81 = 120.