For the following geometric sequence find the recursive formula and the 5th term in the sequence. in your final answer, include all of your work. {-4, 12, -36, }

The nth term for the geometric sequence is given by:

where,

is the first term

r is the common ratio term

n is the number of terms.

Given the sequence:

-4, 12, -36,......

This is a geometric sequence with   and  

Since,

,

ans so on...

Substitute this in [1] we have;

Substitute n = 5 we have;

⇒

Recursive formula for the geometric sequence is given by:

Substitute the given values we have;

Therefore, the recursive formula and the 5th term in the sequence is,

;

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.