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:

3,9,27,81,2433, 9, 27, 81, 243

To identify a pattern, let's examine the relationship between consecutive terms:

  1. First Term to Second Term: 9÷3=39 \div 3 = 3
  2. Second Term to Third Term: 27÷9=327 \div 9 = 3
  3. Third Term to Fourth Term: 81÷27=381 \div 27 = 3
  4. Fourth Term to Fifth Term: 243÷81=3243 \div 81 = 3

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:

243×3=729243 \times 3 = 729

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:

  1. What would be the 8th term in this sequence?
  2. How can the general formula for the nnth term of a geometric sequence be derived?
  3. What is the sum of the first 5 terms of this sequence?
  4. How does changing the common ratio affect the sequence?
  5. 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 nn.

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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