anonymous
  • anonymous
Please help me with my math question??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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OakTree
  • OakTree
What's the question?
anonymous
  • anonymous
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)
OakTree
  • OakTree
Basically this is a plug-and-chug question. If you use n=2, plug it into all of the equations and eliminate the ones that don't work. Then move on to n=3, et cetera.

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anonymous
  • anonymous
i still dont get it?
OakTree
  • OakTree
Let me take you through the first step. So if n=2, the first formula gives us \[a_{2} = a_{2-1} + 2(2-1)\]which simplifies to \[a_{2} = a_{1} + 2\]But a1 is zero, as we know, so we have \[a_2 = 0\]So we know that the first formula is wrong.
anonymous
  • anonymous
where are you getting n=2?
OakTree
  • OakTree
Wait - sorry, it should say a2 = 2. But it's still wrong. And n=2 is saying that there are two children.
anonymous
  • anonymous
oh my gosh im so mad at myself. im still not getting it :(
OakTree
  • OakTree
That's fine! Let me explain it simply. Basically a recursion uses the previous numbers from the formula to get new ones. So we already know that when we have one kid on the playground, there are zero interactions. This is what we call the base recursion, or the n=1 case. n=1 because there is one kid. Now, if we introduce a new kid, we have a new n. Our n now equals 2. So we plug in n=2 to our first formula. The formula says that \[a_2 = a_{2-1} + 2(2-1)\]or\[a_2 = a_1 + 2\]In other words, the number of interactions when there are two kids is two more than the number of interactions when you have one kid. But the numbers we have say that there should be 1 interaction, not two, so we know this formula is wrong. Does that make sense now?
OakTree
  • OakTree
And don't freak out if I leave for a moment or two - I'm switching between you and someone else right now.
anonymous
  • anonymous
ok let me figure this out and tell me if im r ght:) thank you so much for helping me:)
OakTree
  • OakTree
No problem at all.
anonymous
  • anonymous
i dont even know how to solve the equation after i plug everything in :(
OakTree
  • OakTree
Show me your work. And by the way, your formulas in the original question are confusing me a little. Could you maybe rewrite them now? Because a. and c. look the same, and b. looks the same as a. and c. but rearranged.

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