Math Problem Statement
Hunter, a recreational SCUBA diver, begins his ascent to the surface at a constant rate. After 1 minute, he is at a depth of -53 feet. After the 2nd minute, his depth is -52 feet, and a minute later his depth is -51 feet. After the 4th minute, he is at -50 feet, and one minute after that his depth is -49 feet. Classify the sequence by completing the sentence.
Solution
The problem describes a diver's ascent with the following depths at consecutive minutes:
- 1st minute: -53 feet
- 2nd minute: -52 feet
- 3rd minute: -51 feet
- 4th minute: -50 feet
- 5th minute: -49 feet
The sequence of depths is .
Part A: Common Difference
The difference between consecutive terms is constant: Since the difference is the same for each pair of consecutive terms, the sequence has a common difference. This makes it an arithmetic sequence.
Correct Answer:
- (A) The sequence has a common difference.
- (B) The sequence is arithmetic.
Would you like further details or clarification?
Here are 5 related questions:
- What is a common difference in arithmetic sequences?
- How do you find the next term in an arithmetic sequence?
- How do geometric sequences differ from arithmetic sequences?
- How can we find the sum of an arithmetic sequence?
- Can a sequence have both a common difference and a common ratio?
Tip: When identifying a sequence type, always check for consistent differences (arithmetic) or ratios (geometric).
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Common Difference
Formulas
Arithmetic sequence formula: a_n = a_1 + (n-1)d
Theorems
Arithmetic Sequence Definition
Suitable Grade Level
Grades 6-8