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Patterns P and Q are generated using these rules.

​Pattern P: Start with 2 and add 3.
Pattern Q: Start with 2 and add 2.
The first two ordered pairs generated by these rules are (2, 2) and (5, 4). Enter the fifth ordered pair generated from corresponding terms of Pattern P and Pattern Q.

1 answer

To generate the ordered pairs for Patterns P and Q, we can follow the rules defined for each pattern.

Pattern P: Start with 2 and add 3.

  • 1st term: \(2\)
  • 2nd term: \(2 + 3 = 5\)
  • 3rd term: \(5 + 3 = 8\)
  • 4th term: \(8 + 3 = 11\)
  • 5th term: \(11 + 3 = 14\)

The ordered pairs from Pattern P are:

  1. (2, 2)
  2. (5, 4)
  3. (8, ?)
  4. (11, ?)
  5. (14, ?)

Pattern Q: Start with 2 and add 2.

  • 1st term: \(2\)
  • 2nd term: \(2 + 2 = 4\)
  • 3rd term: \(4 + 2 = 6\)
  • 4th term: \(6 + 2 = 8\)
  • 5th term: \(8 + 2 = 10\)

The ordered pairs from Pattern Q are:

  1. (2, 2)
  2. (5, 4)
  3. (?, 6)
  4. (?, 8)
  5. (?, 10)

Now we can line up the patterns to get the ordered pairs:

  1. (2, 2)
  2. (5, 4)
  3. (8, 6)
  4. (11, 8)
  5. (14, 10)

The fifth ordered pair:

The fifth ordered pair generated from corresponding terms of Pattern P and Pattern Q is (14, 10).