1) the sum of an infinite geometric series is three times the first term. Find the common ratio of this series.

2) in a geometric sequence, the fourth term is 8 times the first term. The sum of the first 10 terms is 2557.5. Find the 10th term of this sequence.

3) a large company created a phone tree to contact all employees in case of an emergency. Each of the five Vice Presidents calls five employees, who in turn each call five other employees, and so on. How many rounds of phone calls are needed to reach all 2375 employees?

4) a geometric sequence has all positive terms. The sum of the first two terms is 15 and the sum to infinity is 27.
A. Find the value of the common ratio.
B. Hence, find the first term.

5) The first three terms of an infinite geometric sequence are m - 1, 6, m + 8.
A. Write down two expressions for r.
B. i. Find two possible values of m
ii. Hence, find two possible values of r.
C. i. Only one of these r values forms a geometric sequence where an infinite sum can be found. Justify your choice for r.
ii. Hence, calculate the sum to infinity.