18.4. Counting Solutions to Equations

Try these first

1. 1.

   Define a strictly increasing sequence.

   Hint

   Think about ordering numbers from smallest to largest.

2. 2.

   What is a subsequence?

   Hint

   You can pick numbers that are not next to each other.

3. 3.

   What defines a strictly increasing sequence?

   • A sequence where numbers are random
   • A sequence where numbers decrease
   • A sequence where each number is greater than the previous one

   Hint

   Think about how a mountain would look in terms of height.

4. 4.

   Is it possible to have a strictly decreasing sequence with only two elements?

   • True
   • False

   Hint

   Consider two numbers, one larger and one smaller.

5. 5.

   Create a sequence with 10 distinct integers and show the largest increasing subsequence.

   Hint

   Start with the smallest number and find others that fit the increasing condition.

6. 6.

   Given the integers 5, 15, 10, 20, generate a strictly decreasing sequence and evaluate its properties.

   Hint

   What is the largest number? Start there and descend.