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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a subsequence.
💡 Hint: Think about examples of both sequences and subsequences.
Question 2
Easy
Is the sequence [4, 3, 2, 1] strictly increasing or decreasing?
💡 Hint: Check the relationship between each consecutive term.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is a strictly increasing sequence?
- A sequence where each term is less than the following term
- A sequence where each term is greater than the previous term
- A sequence sorted in descending order
💡 Hint: Look out for terms relative to one another.
Question 2
True or False: Every sequence of n + 1 distinct real numbers contains a decreasing subsequence of length n + 1.
- True
- False
💡 Hint: Consider subsequences formed from increasing distinct numbers.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the sequence [9, 7, 5, 8, 10], demonstrate that there exists either a strictly increasing or decreasing subsequence.
💡 Hint: Look at the sequence order closely, not all need to be taken together.
Question 2
Using a custom sequence of 7 distinct numbers, explain how you can derive an increasing subsequence of at least 5.
💡 Hint: Choose wisely to increase; several must be smaller than your larger picks.
Challenge and get performance evaluation