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:

  1. 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:

  1. Part A: "have a common difference."
  2. Part B: "arithmetic."

Would you like more details about arithmetic sequences or have further questions?

Five Related Questions:

  1. How do you differentiate between arithmetic and geometric sequences?
  2. How can you find the common difference of an arithmetic sequence?
  3. What formula determines the nn-th term in an arithmetic sequence?
  4. How do arithmetic sequences appear in real-world financial problems?
  5. 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