what is the pattern rule for 100 198 295 391
check the differences:
98, 97, 96, ...
so, what do you think?
start at 100, add 95
To find the pattern rule for the given numbers:
Step 1: Calculate the difference between each consecutive pair of numbers.
- Difference between 198 and 100: 98
- Difference between 295 and 198: 97
- Difference between 391 and 295: 96
Step 2: Notice that the differences are decreasing by 1 each time. This indicates that the pattern is likely an arithmetic sequence, where the common difference reduces by 1 each time.
Step 3: Confirm the pattern by subtracting the common difference from each number:
- 198 - 98 = 100
- 295 - 97 = 198
- 391 - 96 = 295
Step 4: Since the pattern confirms, we can conclude that the pattern rule for these numbers is an arithmetic sequence with a common difference decreasing by 1 each time. Starting from 100, the formula can be written as:
nth term = 100 + (n - 1)(-1)
where n represents the position of the term in the sequence.
To identify the pattern rule for a given set of numbers, we need to examine the differences between the terms. Let's calculate the differences between the consecutive terms in the given sequence:
198 - 100 = 98
295 - 198 = 97
391 - 295 = 96
The differences between the terms are decreasing by 1 each time. Based on this pattern, it appears that the sequence is being generated by subtracting a decreasing number from each term.
To further verify this rule, let's calculate the next term:
391 + (96 - 1) = 486
By subtracting 1 from the previous difference of 96, we obtain 95. Adding this to the last term gives us 486, which matches with the next term in the sequence.
Therefore, the pattern rule for the given sequence is to add the difference, which decreases by 1 each time, to the previous term.