







a^(2^n) 
20101022 

From Tim: I am trying to understand a^(2^n).
The hint they give is a^(2^(n+1)) = (a^(2^n))^2
I am writing a program that will solve a^(2^n) recursively but need to
understand the power before I begin.
I am currently pursuing writing (a) x (a^(2^(n1))) where the
(a^(2^(n1))) would be the recursive function call a n approaches 0.
Once n is 0, the result would be multiplied by a two more times.
Anyway, explaining these powers would be appreciated. I will most likely
complete the program before the answer but I want to understand the
logic of these powers. Thank you, Tim Answered by Stephen La Rocque. 





3,6,10,15,and 21 
20080928 

From jarred: i am currently stumped on a math project that requires me to find out the recursive formula for a sequence of numbers. the numbers in the sequence are 3,6,10,15,and 21. Thank you for your time. Answered by Walter Whiteley. 





A recursive formula for 9, 18, 36, 27, ... 
20080605 

From Rita: I am having trouble understanding how to write formulas (I should say create formulas) from a given sequence.
It does not matter what sort of sequence it is. The confusion remains.
I have not found a textbook or easy math book that explains this process for the average Joe to grasp.
Here are the two questions:
(1) Write a recursive formula for the sequence
9, 18, 36, 72, ...
(2) Write a recursive formula for the sequence
3, 3(sqrt{3}), 9, 9(sqrt{3}) Answered by Penny Nom. 





A functional equation 
20021014 

From Rob: Let f be a function whose domain is a set of all positive integers and whose range is a subset of the set of all positive integers with these conditions: a) f(n+1)>f(n)
b) f(f(n))=3(n) Answered by Claude Tardif. 





2=the square root of (2 + the square root of (2 + the square root of (2 +...))) 
20011105 

From Cynthia: justify algebreically, that: 2=the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + and so on, ....... Answered by Penny Nom. 





Population growth 
20010501 

From Gina: Suppose the population of a country increases at a steady rate of 3% a year. If the population is 50 million at a certain time, what will it be 25 years later? Define the recurrence relation that solves this problem. Answered by Penny Nom. 





A sequence defined recursively 
20010501 

From A student: A sequence s is defined recursively as follows: s_{0}=1 s_{1}=2 s_{k}=2s_{k2} for all integers  Compute s2,s3,s4... to guess an explicit formula for the sequence sk. Answered by Penny Nom. 





A sequence of even terms 
20010429 

From A student: A sequence c is defined recursively as follows: c0 = 2 c1 = 4 c2 = 6 ck= 5ck3 for all integers Prove that cn is even for all integers. Answered by Leeanne Boehm and Penny Nom. 





Cutting a Pizza 
19980909 

From Woody: what is the greatest number of pieces of pizza you can form if you use five straight cuts to cut the pizza? answer given is 16. please draw a diagram of the answer. thanks, woody Answered by Penny Nom. 

