Math Problem Statement

Find the next three terms 32, 16, 8, 4, 2

Solution

The given sequence is: 32, 16, 8, 4, 2.

To find the next three terms, observe the pattern. Each term is half of the previous one, meaning the sequence follows a constant ratio of 1/2.

Thus, continuing the sequence:

  • Next term: 2×12=12 \times \frac{1}{2} = 1
  • Term after that: 1×12=0.51 \times \frac{1}{2} = 0.5
  • Third term: 0.5×12=0.250.5 \times \frac{1}{2} = 0.25

So, the next three terms are: 1, 0.5, 0.25.

Would you like more details, or do you have any questions?

Here are some related questions:

  1. What is the general term (nth term) for this sequence?
  2. Can this sequence be classified as geometric or arithmetic?
  3. How do geometric sequences differ from arithmetic ones?
  4. What would happen if the ratio was negative instead of positive?
  5. How do you sum an infinite geometric series?

Tip: The sum of an infinite geometric series can be found if the common ratio is between -1 and 1.

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Math Problem Analysis

Mathematical Concepts

Sequences
Geometric Progression

Formulas

Next term in a geometric sequence: a * r
General term: a_n = a * r^(n-1)

Theorems

Geometric Sequence Theorem

Suitable Grade Level

Grades 6-8