Christopher wrote the number pattern below. The first term is 8. 8, 6, 9, 7, 10, … What is a rule for the pattern?
The Correct Answer and Explanation is:
The given number pattern is: 8, 6, 9, 7, 10, …
To find a rule for the pattern, let’s look at the changes between the numbers:
- From 8 to 6: Subtract 2
- From 6 to 9: Add 3
- From 9 to 7: Subtract 2
- From 7 to 10: Add 3
So, the pattern alternates between subtracting 2 and adding 3.
Rule:
- Start with 8.
- Subtract 2 from the current number, then add 3 to the result. Repeat this process.
We can express this rule as:
- For odd positions (1st, 3rd, 5th, …), subtract 2.
- For even positions (2nd, 4th, 6th, …), add 3.
Example of how the rule works:
- Start with 8 (1st term).
- 8 − 2 = 6 (2nd term).
- 6 + 3 = 9 (3rd term).
- 9 − 2 = 7 (4th term).
- 7 + 3 = 10 (5th term).
- 10 − 2 = 8 (6th term).
This alternating process (subtracting 2, adding 3) continues indefinitely.
Conclusion:
The rule for the pattern is that you alternate between subtracting 2 and adding 3 to the previous number.
