Math Problem Statement

Instructions: Identify the word described by the following statement.

The constant value which is multiplied by each term in a geometric sequence to obtain the next term.

Solution

The word described by the statement is "common ratio."

In a geometric sequence, the common ratio is the constant value by which each term is multiplied to obtain the next term.

Would you like further details on this concept or have any questions?

Here are 5 related questions to consider:

  1. How do you calculate the common ratio in a geometric sequence?
  2. What is the formula for the nth term of a geometric sequence?
  3. How does the common ratio affect the growth or decay of a sequence?
  4. Can the common ratio be a negative number, and what effect does that have?
  5. What is the difference between arithmetic and geometric sequences?

Tip: In geometric sequences, the common ratio remains constant, while in arithmetic sequences, the difference between terms is constant.

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Math Problem Analysis

Mathematical Concepts

Algebra
Sequences and Series
Geometric Sequences

Formulas

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

Theorems

Geometric sequence theorem

Suitable Grade Level

Grades 8-10