Find a pattern in each number sequence below. Then use your pattern to generate the next five numbers in the sequence. Explain the pattern.

1. $2,5,3,6,4,$ ____, ____, ____, ____, ____

• Hint 1 (a):

  Do you see any immediate patterns?

  Hint 2 (a):

  Try different methods to see if you can find any patterns. Ex. Add, subtract, multiply, and divide the second number by the first, the third number by the second, etc.
  
  Do you see any patterns now?

  Answer (a):

  There are two possible approaches to this problem:
  
  1. You may notice that every other number is a consecutive counting number
  
  2. Or you may find that adding three to the first number is the second number, and subtracting two from the second number is the third number, and so on.

2. $100,99,97,94,90,$ ____, ____, ____, ____, ____

• Hint (b):

  Use the method presented in part (a).