Suppose at 8:00 in the morning you tell your best friend a secret. At 8:10, your best friend tell two other people your secret. then those two each tell two others 10 minutes later. This continues all morning long, with every person telling two others every ten minutes who hadn't yet been told . How many people would know by 10:30 am?

Question

campbell_st · Answer

well its a geometric sequence 

time       8:00     8:10     8:20     8:30  8:40
people       1         2         4          8       16

so there are 16 time periods..... a = 1 and r =2

use the sum of a geometric series to get the answer

$$S-{n} = \frac{a(1 - r^n)}{1 - r}$$