Continue the pattern and write a pattern rule.
1,1,2,4,7,11,..,..
I'm really confused about this pattern.
I can give you a hint. The numbers are increasing in an addition pattern. They are added by a number.
The differences between consecutive pairs:
0,1,2,3,4,...
which means the second differences are:
1,1,1,1,...
Thus it can be expressed as a quadratic function
I got this by:
let the function be y = ax^2 + bx + c
and subbed in the points (1,1), (2,1), (3,2), that's all I needed
This gave me three equations in the variables a, b, and c
I assume you know how to solve such a system.
Let me know what you get.
To continue the pattern and find the missing numbers as well as the pattern rule, let's analyze the given numbers:
1, 1, 2, 4, 7, 11, ...
To identify the pattern, we need to observe the differences between consecutive terms:
1, 1, 2, 3, 4, ...
We can see that the differences between terms are increasing by 1 each time:
1, 2, 3, 4, ...
So, to find the missing numbers, we need to continue this pattern of increasing differences:
1, 1, 2, 4, 7, 11, 16, 22, ...
To determine the pattern rule, we can see that the differences between consecutive terms are following a sequence of consecutive numbers: 1, 2, 3, 4, ...
Therefore, the pattern rule for this sequence is adding consecutive numbers:
0 + 1 = 1
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
15 + 6 = 21
So, the missing numbers are 16 and 22, and the pattern rule is to add consecutive numbers starting from 0 to the previous term.