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: , , , , and , as shown on the graph.
Would you like further details or have any questions?
Here are 5 related questions for practice:
- What will be the 6th term of this sequence?
- How would the graph change if the growth factor was greater than 1?
- What is the sum of the first 5 terms of this geometric sequence?
- How can you calculate the 10th term without computing each previous term?
- 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