Math Problem Statement
The explicit formula for a geometric sequence is an = 5 * 2^(n-1). What is the fourth term of the sequence?
Solution
The explicit formula for the geometric sequence is given as:
We are tasked with finding the fourth term of the sequence, which means we need to compute .
Substitute into the formula:
So, the fourth term of the sequence is 40.
Would you like a detailed explanation of how geometric sequences work? Here are 5 related questions that may help expand your understanding:
- How do you find the common ratio in a geometric sequence?
- What is the general formula for the nth term of a geometric sequence?
- How can you determine the sum of the first terms of a geometric sequence?
- What is the difference between geometric and arithmetic sequences?
- How would you find the fifth term of this same sequence?
Tip: Always ensure to substitute the correct value of in the explicit formula to find the desired term in any sequence.
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Math Problem Analysis
Mathematical Concepts
Geometric Sequence
Exponential Functions
Sequences and Series
Formulas
an = 5 * 2^(n-1)
Theorems
Geometric Sequence Formula
Suitable Grade Level
Grades 9-12