18.4.3. Combining Solutions

Try these first

1. 1.

   Define a strictly increasing sequence.

   Hint

   Think about how consecutive numbers relate to each other.

2. 2.

   What is a subsequence?

   Hint

   Consider how you might skip elements in a list.

3. 3.

   What defines a strictly increasing sequence?

   • Every term is equal
   • Each term is greater than the last
   • Each term is lesser than the last

   Hint

   Focus on the relationship between terms.

4. 4.

   True or False: A subsequence must consist of consecutive elements from the original sequence.

   • True
   • False

   Hint

   Think about selection freedom.

5. 5.

   Given the sequence (2, 4, 1, 3, 5, 6), identify possible strictly increasing and decreasing subsequences.

   Hint

   Focus on selecting numbers maintaining their ordering.

6. 6.

   Construct a sequence of 10 distinct integers ensuring that there exists a subsequence of length 5 that is either increasing or decreasing.

   Hint

   Plan a sequence that varies in both directions.