Calculating a Progression
Not what you're looking for?
A king in ancient times agreed to award the inventor of chess with one grain of wheat on the first of the 64 squares on a chess board. On the second square the king placed two grains, on the third square he placed 4 grains and on the fourth square he placed 8 grains of wheat. If the amount of wheat continued to double in this manner how many grains of wheat would there be on the 14th square? Also, find the total number of grains of wheat on the board at the time you get to square 14 and tell what their weight is in pounds. (Assume that each grain of wheat weighs 1/7000 of a pound).
Purchase this Solution
Solution Summary
This solution provides steps to find the number of grains of wheat there would be.
Solution Preview
Solution. Denote by a(n) the number of grains in the nth square. Then we have
a(1)=1, a(2)=2, a(3)=4, a(4)=8, ...
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Probability Quiz
Some questions on probability
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.