Practice Initial Conditions (16.1.5) - Valid Sequences Analysis - Discrete Mathematics - Vol 2

Practice: Initial Conditions

Lesson 16.1.5Valid Sequences Analysis

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8 questions

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2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define a valid sequence in your own words.
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Think about the starting and ending numbers and the rules of increasing order.
Question 2.
What is a recurrence relation?
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It connects current values with past values.
3Question 3.
What does a valid sequence consist of?
- Starts and ends with numbers
- contains any numbers in between
- Starts with one number and ends with another in strictly increasing order
- A random sequence of numbers
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Consider the definition of valid sequences.
4Question 4.
Is the following statement True or False? 'Initial conditions are merely optional in recurrence relations.'
- True
- False
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Think about why we need starting points for sequences.
Question 5.
Suppose you have a sequence defined recursively. If s(1) = 1, s(2) = 1, and s(n) = s(n-1) + s(n-2) for n > 2, what is s(5)?
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Work backwards from the values you know.
Question 6.
Create a sequence ending with '5' and starting with '1', listing all the valid strictly increasing sequences.
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Count valid combinations based on the defined rules.

4 more questions in this section. Enroll free to practise them all.