Math Problem Statement

write the pattern of number sequence using the words: 3,18,108,648,3888,....

Solution

The number sequence provided is: 3, 18, 108, 648, 3888, ...

To describe the pattern using words:

  • Start with 3.
  • Each subsequent number is obtained by multiplying the previous number by 6.

Here’s the step-by-step explanation:

  1. The first number is 3.
  2. Multiply 3 by 6 to get 18.
  3. Multiply 18 by 6 to get 108.
  4. Multiply 108 by 6 to get 648.
  5. Multiply 648 by 6 to get 3888.

This multiplication by 6 continues for each following term.

Would you like more details or clarification on this pattern?

Here are 5 related questions to explore:

  1. What would the next number in the sequence be after 3888?
  2. Can you express the nth term of this sequence as a general formula?
  3. How does the growth of this sequence compare to a geometric progression with a different ratio?
  4. If the first number were changed to a different starting value, how would the sequence change?
  5. Can you find a sum of the first five numbers of the sequence?

Tip: In sequences involving constant multiplication, you're often dealing with geometric progressions. The common ratio is key to predicting future terms.

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Math Problem Analysis

Mathematical Concepts

Geometric Sequences
Multiplication
Exponential Growth

Formulas

Geometric sequence formula: a_n = a_1 * r^(n-1)

Theorems

Geometric progression theorem

Suitable Grade Level

Grades 6-8