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

Given: No. of people receiving flyer is 6 (in first hr) and number of people receiving flyer by the six people is 6 x 6 = 36(in the 2nd hour)

To find: The number of people who receive a stack of flyers, not including the initial person, in the first five hours.

Solution:

• So, according to question, we can see that the pattern is repeating, so:

             people receiving flyer by the 36 people :

             36 x 6 = 216 (in 3rd hr)

             people received flyer by 72 people :

             216 x 6 = 1296 (in  4th hr)

             people receiving flyer by 432 people :

             1296 x 6 = 7776

             (in 5th hr)

• So, the sequence comes out to be:

             1, 6, 36, 216, 1296, 7776

• From above sequence we can see that common ratio is 7, so its a geometric progression.

• So sum of sequence is: a ( 1 - r^n) / 1 - r

           here a = 6 and r = 6

           sum = 6 x (1-6^6) / 1-6

• After calculating, it comes out to be: 9330

• So the number of people who receives flyer are 9330.

Answer:

              So the number of people who receives flyer are 9330.