4 answers
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a(1) = 0
a(n+1) = a(n)+(2n-1)
or,
a(n) = (n-1)^2
A playground is being designed where children can interact with their friends in certain combinations.
If there is 1 child, there can be 0 interactions.
If there are 2 children, there can be 1 interactions.
If there are 3 children, there can be 4 interactions.
If there are 4 children, there can be 9 interactions.
Which recursive equation represents the pattern?
Steve
answered7 years ago
Steve
answered7 years ago
Thank you
Could it be written as a(n)=a(n-1)+2^n-3
Steve ®
answered7 years ago
Did you even check out your idea?
a(1) = 0
a(2) = a(1) + 2^2-3 = 0+1 = 1
a(3) = a(2) + 2^3-3 = 1+5 = 6
a(4) = a(3) + 2^4-3 = 6+13 = 19
Explain Bot
answered1 year ago
To find the recursive equation that represents the pattern of interactions, we need to analyze the given information.
First, let's list the number of interactions for each number of children:
- 1 child: 0 interactions
- 2 children: 1 interaction
- 3 children: 4 interactions
- 4 children: 9 interactions
We can observe that the number of interactions for each case is increasing by adding a squared number. For example, when there are 2 children, there is 1 interaction (1^2), and when there are 3 children, there are 4 interactions (2^2). Similarly, when there are 4 children, there are 9 interactions (3^2).
Based on this observation, we can conclude that the recursive equation representing the pattern is:
𝐈(𝑛) = 𝐈(𝑛 − 1) + 𝑛^2
Where 𝐈(𝑛) represents the number of interactions for 𝑛 children, and 𝑛 represents the number of children. This equation states that the number of interactions for 𝑛 children is equal to the number of interactions for 𝑛-1 children plus 𝑛^2 (the square of the number of children).