What Are the Patterns?

4.15.1 What Are the Patterns?

4.15.1 • What Are the Patterns?

Warm Up

Examine the patterns of numbers given below.

  • 40, 120, 360, 1,080, 3,240
  • 2, 8, 32, 128, 512
  • 1,000, 500, 250, 125, 62.5
  • 256, 192, 144, 108, 81
1.

What do you notice?

Compare your answers:

  • The first two sequences are increasing, and the second two are decreasing.
  • The next number in the list comes from always multiplying the previous number by the same value.
  • If we choose a number in the list and divide it by the previous number, we always get the same value.
2.

What do you wonder?

Compare your answers:

  • Why do all the sequences start with even numbers?
  • Will the last sequence eventually have decimal numbers like the one before it since it is also decreasing?
  • Are these sequences related in some way?
  • Is the next term of the second sequence 1,024?