Aplayground 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?

Recursive equation for the pattern followed is given by,

In the question,

The number of interaction for 1 child = 0

Number of interactions for 2 children = 1

Number of interactions for 3 children = 5

Number of interaction for 4 children = 14

So,

We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

Therefore, on checking, we observe that,

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

At,

n = 1

which is true.

At,

n = 2

Which is also true.

At,

n = 3

Which is true.

At,

n = 4

This is also true at the given value of 'n'.

Therefore, the recursive equation for the pattern followed is given by,

the answer will be

the answer is simply just 6n add the two together as they have an n