Question

You collect pennies. you start with one penny and double the number of pennies you have each day for the next 27 days. how many pennies will you have at the end of 27 days?

Answer 1

Imagine, at the first day you have only one penny. Then tomorrow you have 2 pennies, next day you have 4 (2x2), next day you have 8 (4x2), next day you have 16 (8x2).... and so forth.

It looks like geometric sequence isn't it? (the ratio between the number of pennies that you have from the 2nd day and the 1st day is 2)

So, by using geometric sequence theorem we can total those pennies until day-27

S (total pennies at day-27) = (1)(2^27-1) / 2-1 = 2^26 pennies

So, you have 2^26 pennies.. a big number of pennies huh?=))


{The formula is: S = a( r^n-1) / r-1
Where:
a= the number of pennies that you've got at the 1st day
n= number of days you spent to collect those pennies)
r= the ratio of the number of pennies}