Question

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.

Answer 1

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)**.