Math Problem Statement
Identify a pattern in the given list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) 3, 9, 27, 81, 243
Solution
The sequence given is:
To identify a pattern, let's examine the relationship between consecutive terms:
- First Term to Second Term:
- Second Term to Third Term:
- Third Term to Fourth Term:
- Fourth Term to Fifth Term:
Each term is obtained by multiplying the previous term by 3. Therefore, the pattern is a geometric sequence with a common ratio of 3.
To find the next number in the sequence:
So, the next number in the sequence is 729.
Would you like a detailed explanation of geometric sequences or have any questions?
Here are 5 relative questions to consider:
- What would be the 8th term in this sequence?
- How can the general formula for the th term of a geometric sequence be derived?
- What is the sum of the first 5 terms of this sequence?
- How does changing the common ratio affect the sequence?
- Can you identify a different pattern in the sequence that gives a different next term?
Tip: In geometric sequences, each term is a constant multiple of the previous term, which makes them predictable and easy to calculate for large .
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Math Problem Analysis
Mathematical Concepts
Geometric Sequences
Formulas
nth term of a geometric sequence
Theorems
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Suitable Grade Level
Grades 7-9