Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: From Patterns to Generalizations: Sequences and Series, Exercise 32: Exercise 1K

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?

A geometric sequence has all positive terms. The sum of the first two terms is $15$ and the sum to infinity is $27$. Find the value of the common ratio.

A geometric sequence has all positive terms. The sum of the first two terms is $15$ and the sum to infinity is $27$. Find the first term.

The first three terms of an infinite geometric sequence are $m-1, 6, m+8$. Write down two expressions for $r$.

The first three terms of an infinite geometric sequence are $m-1, 6, m+8$. Find two possible values of $m$.

The first three terms of an infinite geometric sequence are $m-1, 6, m+8$. Find two possible values of $r$.

The first three terms of an infinite geometric sequence are $m-1, 6, m+8$. Find two possible values of $r$. Only one of these $r$ values forms a geometric sequence where an infinite sum can be found. Justify your choice for $r$.

The first three terms of an infinite geometric sequence are $m-1, 6, m+8$. Calculate the sum to infinity.