Given below are two sets of numbers. Both the sets are formed using the same mathematical equations or follow a common pattern. Which of the given options follows the same set of mathematical equations or patterns as the sets given in the question? 1333-1730-2199-2746-3377 218-345-514-731-1002
3-10-29-66-127
Let's analyze the given number sets to find the underlying pattern:
Set 1: 1333-1730-2199-2746-3377
Differences between consecutive numbers:
- 1730 - 1333 = 397
- 2199 - 1730 = 469
- 2746 - 2199 = 547
- 3377 - 2746 = 631
Differences between the differences:
- 469 - 397 = 72
- 547 - 469 = 78
- 631 - 547 = 84
There's a constant difference of 6 in the second differences.
Set 2: 218-345-514-731-1002
Differences between consecutive numbers:
- 345 - 218 = 127
- 514 - 345 = 169
- 731 - 514 = 217
- 1002 - 731 = 271
Differences between the differences:
- 169 - 127 = 42
- 217 - 169 = 48
- 271 - 217 = 54
There's a constant difference of 6 in the second differences.
Now let's check the options:
Option 2: 3-10-29-66-127
Differences:
- 10 - 3 = 7
- 29 - 10 = 19
- 66 - 29 = 37
- 127 - 66 = 61
Differences of differences:
- 19 - 7 = 12
- 37 - 19 = 18
- 61 - 37 = 24
Differences of differences of differences:
- 18 - 12 = 6
- 24 - 18 = 6
This set shows a constant difference of 6 in the third differences, similar to the pattern in the original sets.
Therefore, the correct option is 3-10-29-66-127.
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