Math Problem Statement
finish sentence
The price of shares in a popular stock started at $27.50 per share and dropped by $0.25 every two hours. Classify the sequence as arithmetic or geometric and explain your reasoning.
Solution
The question asks you to classify a sequence related to stock prices, as seen from the options and text. Let's carefully interpret the content.
From the problem:
- The share price drops as follows:
- Initial price: $27.50
- After 2nd hour: $27.25
- After 4th hour: $27.00
- It keeps dropping by the same pattern ($0.25 per interval).
Identifying the sequence type:
- Arithmetic sequences have a common difference (each term changes by adding or subtracting a fixed number).
- Geometric sequences have a common ratio (each term changes by multiplying by a fixed number).
Here:
- The sequence decreases by a constant difference of -0.25 each time (27.50 → 27.25 → 27.00).
Thus, this is an arithmetic sequence.
Correct Completion:
- Part A: "have a common difference."
- Part B: "arithmetic."
Would you like more details about arithmetic sequences or have further questions?
Five Related Questions:
- How do you differentiate between arithmetic and geometric sequences?
- How can you find the common difference of an arithmetic sequence?
- What formula determines the -th term in an arithmetic sequence?
- How do arithmetic sequences appear in real-world financial problems?
- Can an arithmetic sequence ever increase? If so, how?
Tip: In an arithmetic sequence, if the common difference is negative, the sequence decreases steadily.
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Math Problem Analysis
Mathematical Concepts
Sequences
Arithmetic Sequences
Geometric Sequences
Formulas
Arithmetic Sequence Formula: a_n = a_1 + (n - 1)d
Theorems
In arithmetic sequences, the difference between consecutive terms is constant.
Suitable Grade Level
Grades 7-9