Question

Declan and Dalton use patterns. Declan's pattern uses the rule add 3 and starts at 6. Dalton's pattern uses the rule add 5 and starts at 3. Complete the statement/s that show the relationship between the two patterns. Choose all that apply.

1. The two patterns have terms in common.
2. The two patterns do NOT have terms in common.
3. Declan's pattern only has odd numbers.
4. Declan's pattern only has even numbers.
5. Declan's pattern has both odd and even numbers.
6. Dalton's pattern only has odd numbers.
7. Dalton's pattern has only even numbers.
8. Dalton's pattern has both odd and even numbers.
9. Other: _______________________

Answer 1

Declan's pattern starts at 6 and adds 3, resulting in a sequence containing both odd and even numbers. Dalton's pattern starts at 3 and adds 5, also yielding both odd and even numbers. Both patterns have terms in common, indicating a relationship between them.

Step-by-step explanation:

Declan's pattern starts at 6 and follows the rule add 3. Therefore, Declan's sequence is 6, 9, 12, 15, 18, ... This pattern contains both odd and even numbers.

Dalton's pattern starts at 3 and follows the rule of adding 5. Thus, Dalton's sequence is 3, 8, 13, 18, 23, ... This pattern also contains both odd and even numbers.

By examining both patterns, we can see they have terms in common; for example, the number 18 appears in both patterns. Therefore, Declan's pattern does not consist of only odd or even numbers, and similarly, Dalton's pattern includes both odd and even numbers. Additionally, the patterns of Declan and Dalton intersect, reflecting a relationship between the two patterns.