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?

135

84

93

108

Question

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?

 135

 84

 93

 108

rsadhvika · Answer

observe the pattern :-

$a_{n} = a_{n-1} + 3(n-1)$

rsadhvika · Answer

find the interactions upto 9 childern using above recursive relation

anonymous · Answer

what do i plug in for the variables?

rsadhvika · Answer

lets find number of interactions for 5 children :-
$a_{5} = a_{5-1} + 3(5-1) $

$a_{5} = a_{4} + 3(4) $

$a_{5} = 18 + 12 $

$a_{5} = 30 $

rsadhvika · Answer

similarly, find a6, a7, a8 and a9

anonymous · Answer

where did the 18 come from?

rsadhvika · Answer

good q, look at the orignial quesiton

rsadhvika · Answer

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

anonymous · Answer

mhmm