Answer:
Part a) The rule of the sequence is 
Part b) The height of the ball will be 
Step-by-step explanation:
Part a) Write a rule for the sequence using centimeters. The initial height is given by the term n = 1.
we know that
In a <u>Geometric Sequence</u> each term is found by multiplying the previous term by a constant called the common ratio (r)
In this problem we have a geometric sequence
Let
n-----> the number of path
a1 ----> is the initial height
r -----> the common ratio
we have


The rule for the sequence is equal to

substitute

Part b) What height will the ball be at the top of the third path?
For n=3
substitute in the equation


Answer:
The 50th term is 288.
Step-by-step explanation:
A sequence that each term is related with the prior by a sum of a constant ratio is called a arithmetic progression, the sequence in this problem is one of those. In order to calculate the nth term of a setence like that we need to use the following formula:
an = a1 + (n-1)*r
Where an is the nth term, a1 is the first term, n is the position of the term in the sequence and r is the ratio between the numbers. In this case:
a50 = -6 + (50 - 1)*6
a50 = -6 + 49*6
a50 = -6 + 294
a50 = 288
The 50th term is 288.
Prime numbers are numbers that only have a factor of one and its self.