# SOLUTION: Hello. I would appreciate an explanation to the following question: A playground is being designed where children can interact with their friends in certain combinations. If

Algebra ->  Algebra  -> Sequences-and-series -> SOLUTION: Hello. I would appreciate an explanation to the following question: A playground is being designed where children can interact with their friends in certain combinations. If       Log On

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 Algebra: Sequences of numbers, series and how to sum them Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Sequences-and-series Question 495959: Hello. I would appreciate an explanation to the following question: 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 pattern represents the pattern? asubn=asubn-1+2^(n-1) asubn=asubn+(n-1)^2 asubn=asubn+2(n-1) asubn=asubn+(2n-1) So far I have figured out by setting up this basic pattern chart that: n a 1 0 +1 2 1 +4 3 5 +9 4 14 Is the equation always the same? or does it change with the given information. I got this wrong and would appreciate understanding why? I understand how to make derive the sequence information. What if I need the 50th term? I can easily get the ninth term as in the previous question on this assignment. But having trouble understanding how to write the formula. I appreciate you help. This is a wonderful resource for students who take math seriously because the tutors answer the questions so thoroughly. Again, thank you in advance. Justina Answer by Theo(3458)   (Show Source): You can put this solution on YOUR website!the formula that works with the data is as follows: a[n] = a[n-1] + (n-1)^2 here's a table of values based on that formula. the table starts with a[1] being given as 0. ``` n (n-1)^2 a[n] 1 n/a given as 0 2 1^2 = 1 1 + 0 = 1 3 2^2 = 4 4 + 1 = 5 4 3^2 = 9 9 + 5 = 14 5 4^2 = 16 16 + 14 = 30 6 5^2 = 25 25 + 30 = 55 ... ``` you are given that the a[1] = 0 the rest of them are derived from the formula. the same formula is used every time. let me know if this solves the problem for you.