Respuesta :
We are given five hours in this problem, since the first hour was used by the very first person, we can say that only 4 hours of this time was used by every 6 people. The equation is therefore,
n = (6)^4 = 1296
Thus, the number of people who received stack of flyers is 1296.
n = (6)^4 = 1296
Thus, the number of people who received stack of flyers is 1296.
Answer:
Sum = [tex]\frac{6\times (1-6^5)}{1-6}[/tex]
Step-by-step explanation:
We have that,
Number of people receiving flyer by the first person in 1st hour = 6
Number of people receiving flyer by the six people in the 2nd hour=6×6=36
As, we have that the pattern is repeating,
So, the pattern is given by 'The total number of people in the previous hour will distribute the flyer to 6 new people'.
Number of people receiving flyer by the 36 people in the 3rd hour=36×6=216
Number of people receiving flyer by the 72 people in the 4th hour=216×6=1296
Number of people receiving flyer by the 432 people in the 5th hour=1296×6= 7776
Thus, the sequence for the number of people receiving flyers is given by,
1, 6, 36, 216, 1296, 7776
As we see that the common ratio for the geometric sequence is [tex]\frac{72}{12}=6[/tex].
Thus, the sum of the sequence is [tex]\frac{a_{1}(1-r^n)}{1-r}[/tex], where 'r' is the common ratio and [tex]a_{1}[/tex] is the initial term.
As, we need to exclude the initial person.
So, [tex]a_{1}=6[/tex] and [tex]r=6[/tex]
Thus, sum = [tex]\frac{6\times (1-6^5)}{1-6}[/tex]
i.e. Sum = [tex]\frac{6\times (1-7776)}{-5}[/tex]
i.e. Sum = [tex]\frac{6\times (-7775)}{-5}[/tex]
i.e. Sum = [tex]\frac{-46650}{-5}[/tex]
i.e. Sum = 9330
Thus, the number of people receiving the flyers are 9330.
So, the summation used to find the number of flyers is sum is [tex]\frac{6\times (1-6^5)}{1-6}[/tex].