what is the rule for the number pattern 1,2,4,7,11,16
1 + 1 = 2
2 + 2 = 4
4 + 3 = 7
What pattern do you see here?
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To determine the rule for the number pattern 1, 2, 4, 7, 11, 16, we need to observe the differences between consecutive terms. Let's calculate the differences:
2 - 1 = 1
4 - 2 = 2
7 - 4 = 3
11 - 7 = 4
16 - 11 = 5
The differences between consecutive terms are 1, 2, 3, 4, 5. Now, let's analyze these differences.
We see that the differences are increasing by 1 each time. The first difference is 1, the second difference is 2, the third difference is 3, and so on.
Since the differences are increasing, we can conclude that the original number pattern is likely generated by adding consecutive integers starting from 1.
Based on this observation, we can generate the terms of the number pattern by adding the consecutive integers to the previous term. Let's apply this rule:
1 + 1 = 2
2 + 2 = 4
4 + 3 = 7
7 + 4 = 11
11 + 5 = 16
Therefore, the rule for the number pattern 1, 2, 4, 7, 11, 16 is to add consecutive integers starting from 1 to the previous term.
add n to the last term, where n is the order.
1, then add 1
2, then add 2
4, then add 3
7, then add 4
11, then add 5