Question

A flyer is spread by people at a large conference. Within one hour, the first person gives a stack of flyers to six people. Within the next hour, those six people give a stack of flyers to six new people. If this pattern continues, which summation can be used to calculate the number of people who receive a stack of flyers, not including the initial person, in the first five hours?

Answer 1

Sum =
`(6* (1-6^5))/(1-6)`

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
`(72)/(12)=6`.

Thus, the sum of the sequence is
`(a_(1)(1-r^n))/(1-r)`, where 'r' is the common ratio and
`a_(1)` is the initial term.

As, we need to exclude the initial person.

So,
`a_(1)=6` and
`r=6`

Thus, sum =
`(6* (1-6^5))/(1-6)`

i.e. Sum =
`(6* (1-7776))/(-5)`

i.e. Sum =
`(6* (-7775))/(-5)`

i.e. Sum =
`(-46650)/(-5)`

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
`(6* (1-6^5))/(1-6)`.

Answer 2

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.