What Is Geometric Sequence?
A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. This sequence can be expressed as a, ar, ar2, ar3, ar4, and so on, where r ≠ 0. Geometric sequences are used to model simple growth and decay. They can also be used to model compounding interest.
How To Identify A Geometric Sequence?
A geometric sequence can be identified by its common ratio. The common ratio is the number that each term in the sequence is multiplied by to get the next term. If each term is multiplied by the same number, then the sequence is geometric. This can be written as a, ar, ar2, ar3, and so on. The common ratio is the number r.
Examples Of Geometric Sequences
One of the simplest examples of a geometric sequence is the sequence 2, 4, 8, 16, 32, 64, and so on. In this sequence, the common ratio is 2. This means that each term is multiplied by 2 to get the next term. The first term is 2, and each successive term is twice the previous one.
Another example of a geometric sequence is the sequence 4, 12, 36, 108, 324, and so on. In this sequence, the common ratio is 3. This means that each term is multiplied by 3 to get the next term. The first term is 4, and each successive term is three times the previous one.
Which Of The Following Sequences Are Geometric?
There are several sequences that could be geometric. Here are some examples:
- 2, 4, 8, 16, 32, 64, and so on.
- 4, 12, 36, 108, 324, and so on.
- 1, 4, 16, 64, 256, and so on.
- 2, 6, 18, 54, 162, and so on.
In each of these sequences, the common ratio is the same. For example, in the first sequence, the common ratio is 2. This means that each term is multiplied by 2 to get the next term. In the second sequence, the common ratio is 3. This means that each term is multiplied by 3 to get the next term. In the third sequence, the common ratio is 4. This means that each term is multiplied by 4 to get the next term. In the fourth sequence, the common ratio is 6. This means that each term is multiplied by 6 to get the next term.
Conclusion
A geometric sequence is a sequence in which each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. This sequence can be expressed as a, ar, ar2, ar3, and so on, where r ≠ 0. Geometric sequences can be identified by their common ratio. Examples of geometric sequences include 2, 4, 8, 16, 32, 64, and so on; 4, 12, 36, 108, 324, and so on; 1, 4, 16, 64, 256, and so on; and 2, 6, 18, 54, 162, and so on.
