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 3 interactions.
If there are 3 children, there can be 9 interactions.
If there are 4 children, there can be 18 interactions.

How many interactions will there be for 9 children?

A. 135

B. 84

C. 93

D. 108

Answer 1

the interactions are not shown in geometric progressions i think

Answer 2

That's all there is to the question.

Answer 3

@phi

Answer 4

I think it's C

Answer 5

why?

Answer 6

http://openstudy.com/study#/updates/512684bfe4b0111cc68efa29

Answer 7

one way to analyze this is find differences
1 0
3
2 3 3
6
3 9 3
9
4 18

the "second differences" are constant of 3
if it follows the same pattern the first differences are
0,3,6,9,12,15,18,21,24
and the nth entry is the sum of the first n terms.
Example: the 3rd term would be 0+3+6 = 9
and the 4th term: 0+3+6+9= 18

0, 3, 9, 18, 30, 45, 63, 84, 108
1 2 3 4 5 6 7 8 9

a closed-form solution would be to notice that the nth term is
3 ( 0 + 1 + 2 + ... + n-1)
= 3* (n-1)* n/2

for n=9: 3*8*9/2 =108