Math Problem Statement

Make 4 word examples of nth term of geometric sequence

Solution

Here are four word examples related to the nth term of a geometric sequence:

  1. Ratio growth doubles constantly.
  2. Terms increase exponentially each time.
  3. Value multiplies by constant factor.
  4. Sequence progression multiplies regularly.

The nth term of a geometric sequence follows the formula an=a1rn1a_n = a_1 \cdot r^{n-1}, where:

  • ana_n is the nth term,
  • a1a_1 is the first term,
  • rr is the common ratio,
  • nn is the term number.

Would you like more details on this formula?

Related Questions:

  1. How do you find the common ratio in a geometric sequence?
  2. What happens if the common ratio is a fraction?
  3. Can a geometric sequence have negative terms?
  4. How does geometric progression differ from arithmetic?
  5. What are real-life examples of geometric sequences?

Tip: In a geometric sequence, the common ratio between consecutive terms remains constant.

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Math Problem Analysis

Mathematical Concepts

Geometric Sequence
Exponential Growth

Formulas

nth term of geometric sequence: a_n = a_1 * r^(n-1)

Theorems

Geometric progression formula

Suitable Grade Level

Grades 9-12