Math Problem Statement

A geometric sequence g starts at 500 and has a growth factor of 0.6. Sketch a graph of g showing the first 5 terms.

Solution

Here is the graph of the first five terms of the geometric sequence. As expected, the values decrease exponentially, reflecting the growth factor of 0.6.

The terms are: 500500, 300300, 180180, 108108, and 64.864.8, as shown on the graph.

Would you like further details or have any questions?

Here are 5 related questions for practice:

  1. What will be the 6th term of this sequence?
  2. How would the graph change if the growth factor was greater than 1?
  3. What is the sum of the first 5 terms of this geometric sequence?
  4. How can you calculate the 10th term without computing each previous term?
  5. What is the general formula for the sum of an infinite geometric series?

Tip: In a geometric sequence, if the growth factor is less than 1, the terms will gradually approach 0.

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Math Problem Analysis

Mathematical Concepts

Geometric Sequences
Exponential Decay

Formulas

General formula for geometric sequences: g_n = g_1 * r^(n-1)

Theorems

Geometric Sequence Theorem: In a geometric sequence, each term is found by multiplying the previous term by a constant factor.

Suitable Grade Level

Grades 8-10