Questions: 21. Higher Order Thinking In case of an emergency, the school has a calling list so that everyone is called in the least amount of time. Each of the first 3 people on the list calls another 3 people on the list. Then, each of the people in the second group calls another 3 people on the list, and so on. The fifth group of people will make 243 calls. Is this statement accurate? Explain.

Solution Steps

To determine if the statement is accurate, we need to understand the pattern of calls. Each person calls 3 others, forming a geometric progression. We can calculate the number of calls made by the fifth group using the formula for the nth term of a geometric sequence, where the first term \( a = 3 \) and the common ratio \( r = 3 \).

In this scenario, each person on the calling list calls 3 others. This creates a geometric progression where the number of calls made by each group can be expressed as: \[ \text{Calls in group } n = 3^n \] where \( n \) is the group number.

To find the number of calls made by the fifth group, we substitute \( n = 5 \) into the formula: \[ \text{Calls in group 5} = 3^5 = 243 \]

The statement claims that the fifth group will make 243 calls. Since we calculated that the fifth group indeed makes 243 calls, the statement is accurate.

Final Answer