We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

On a calendar, I put 1 grain of sand on May 1st, 2 grains of sand on May 2nd, 4 grains on May 3rd, and so forth, doubling the number of grains each day. On what day will I put down the 500th grain?

GamingKev Feb 15, 2019

#1**+1 **

We can use the sum of a geometric series to solve this

Sum = First term [ 1 - (common ratio)^n ] / [ 1 - common ratio]

The common ratio is 2....and we are trying to find " n".....so we have

500 = 1 [ 1 - 2^n ] / [1 - 2 ]

500 = 1 [ 1 - 2^n ] / [ - 1 ] multiply both sides by -1

- 500 = 1 - 2^n subtract 1 from both sides

-500 - 1 = -2^n

-501 = - 2^n multiply both sides by -1

2^n = 501 take the log of both sides

log 2^n = log 501 and we can write

n * log (2) = log (501) divide both sides by log (2)

n = log (501) / log (2) ≈ 8.96 days

CPhill Feb 15, 2019