Math Problem Statement
Solution
Let's analyze the sequence to determine its explicit formula:
Step 1: Recognize the pattern
- Start with the sequence:
- Notice that each term seems to grow quickly. To confirm, let's check the ratio between consecutive terms.
Since the ratio is constant (), the sequence is a geometric progression.
Step 2: General formula for geometric sequences
The general formula for a geometric sequence is:
- Here:
- (the first term),
- (common ratio).
Substitute into the formula:
Step 3: Match with the options
Looking at the options:
- Option D matches .
Final Answer:
Option D is correct.
Do you want further clarification or a detailed breakdown of any step?
Here are five related questions you may want to explore:
- What is the general formula for a geometric sequence?
- How can you identify a geometric sequence from given terms?
- How do you find the sum of the first -terms of a geometric sequence?
- What is the difference between arithmetic and geometric sequences?
- How do you determine the common ratio of a geometric sequence?
Tip: In geometric sequences, the ratio between consecutive terms remains constant, which simplifies finding the explicit formula.
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Math Problem Analysis
Mathematical Concepts
Geometric Sequences
Explicit Formula
Common Ratio
Formulas
a_n = a_1 * r^(n-1)
Theorems
General formula for geometric sequences
Suitable Grade Level
Grades 9-11
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