21. higher order thinking in case of an emergency, the school has a calling list so that everyone is called…

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.

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.

Answer

Explanation:

Step1: Analyze the pattern

The number of calls forms a geometric sequence where the first - term (a = 3) (since the first group of 3 people make calls) and the common ratio (r=3). The formula for the (n)th term of a geometric sequence is (a_n=a\times r^{n - 1}).

Step2: Substitute (n = 5), (a = 3) and (r = 3) into the formula

We get (a_5=3\times3^{5 - 1}). Using the rule of exponents (a^m\times a^n=a^{m + n}), we have (a_5=3^{1+4}). Since (3^{1 + 4}=3^5), and (3^5=3\times3\times3\times3\times3 = 243).

Answer:

Yes, the statement is accurate.