SOLUTION: 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
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Question 777509: 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 only 1 interaction.
If there are 3 children, there can be 5 interactions.
If there are 4 children, there can be 14 interactions.
Which recursive equation represents the pattern?
a. an = an - 1 + 2(n - 1)
b. an = an - 1 + (n - 1) 2
c. an = an - 1 + 2(n - 1)
d. an = an - 1 + (2n - 1)
I want to know the proccess on how to do this not only the answer.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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 only 1 interaction.
If there are 3 children, there can be 5 interactions.
If there are 4 children, there can be 14 interactions.
Which recursive equation represents the pattern?
Note: There is no magic to finding the answer. You just have
to test each one to see what does and what does not give the answer.
------------------------------
a. an = a(n - 1) + 2(n - 1)
a1 = 0 + 2*0
a2 = 0 + 2*1 = 2 fails at a2
--------------------------------------
b. an = a(n - 1) + (n - 1)^2
a1 = 0 + 0^2 = 0
a2 = 0 + 1^2 = 1
a3 = 1 + 2^2 = 5
a4 = 3 + 3^2 = 12 fails at a4
--------------------------------------
etc...
Cheers,
Stan H.
c. an = a(n - 1) + 2(n - 1)
d. an = a(n - 1) + (2n - 1)
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