Write a rule for the sequence: 18, 16, 13, 9, ...
a. Start with 18, and subtract 2 repeatedly.
b. Start with 10, and add 6 repeatedly.
c. Start with 18, and divide by 2 repeatedly.
d. Start with 18, and add 4 repeatedly.
The correct answer is option a. Start with 18, and subtract 2 repeatedly.
To find the next term in the sequence, we subtract 2 from the previous term:
18 - 2 = 16,
16 - 2 = 14,
14 - 2 = 12,
12 - 2 = 10,
Therefore, the next term would be 10.
To find the rule for the given sequence: 18, 16, 13, 9, ...
Step 1: Look for a pattern between consecutive terms.
If we observe the differences between the terms, we can see that the differences are decreasing by 2 each time. The differences are 2, 3, and 4, respectively.
Step 2: Identify the operation responsible for the pattern.
Since the differences are decreasing, the most likely operation is subtraction.
Step 3: Verify the rule by applying it to the first few terms.
a. Start with 18, and subtract 2 repeatedly:
18 - 2 = 16
16 - 2 = 14
14 - 2 = 12
The first few terms of the sequence match the pattern of subtracting 2.
b. Start with 10, and add 6 repeatedly:
10 + 6 = 16
16 + 6 = 22
22 + 6 = 28
The first few terms of the sequence do not match the pattern of adding 6.
c. Start with 18, and divide by 2 repeatedly:
18 / 2 = 9
9 / 2 = 4.5
The first few terms of the sequence do not match the pattern of dividing by 2.
d. Start with 18, and add 4 repeatedly:
18 + 4 = 22
22 + 4 = 26
The first few terms of the sequence do not match the pattern of adding 4.
Based on the observed pattern and the verification, the correct rule for the sequence is:
a. Start with 18, and subtract 2 repeatedly.