Math Problem Statement

  1. Find the next three terms of each sequence.

a) 3, 6, 12, 24,

Solution

Let's analyze the sequence: 3, 6, 12, 24.

Each term is being multiplied by 2 to get the next term:

6=3×26 = 3 \times 2 12=6×212 = 6 \times 2 24=12×224 = 12 \times 2

So, continuing this pattern:

Next term=24×2=48\text{Next term} = 24 \times 2 = 48 Next term=48×2=96\text{Next term} = 48 \times 2 = 96 Next term=96×2=192\text{Next term} = 96 \times 2 = 192

Therefore, the next three terms of the sequence are:

48,96,19248, 96, 192

Would you like more details or clarification on this?

Here are five related questions to practice:

  1. What are the next three terms of the sequence: 5, 10, 20, 40?
  2. What is the general formula for the sequence 3, 6, 12, 24?
  3. How do you identify a geometric sequence from a given set of terms?
  4. Can this sequence be represented by a different mathematical operation, such as addition or subtraction?
  5. How would the sequence change if each term were multiplied by 3 instead of 2?

Tip: When identifying patterns in a sequence, look for consistent operations (like multiplication, division, or addition) between consecutive terms.

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Math Problem Analysis

Mathematical Concepts

Geometric Sequences
Multiplication Patterns

Formulas

Next term = Previous term × 2

Theorems

Geometric Sequence Theorem

Suitable Grade Level

Grades 6-8