Question 342107: How do you go about finding a pattern in a sequence of numbers? i just keep trying out different numbers but i just sit there for hours and some times i still don't see a pattern. Is there a process for finding a pattern?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How do you go about finding a pattern in a sequence of numbers? i just keep trying out different numbers but i just sit there for hours and some times i still don't see a pattern. Is there a process for finding a pattern?
----------------------
Assume you have a geometric sequence: 1,2,4,8,16,32,,,
---
You are looking for a pattern to describe a(n) which is the nth term.
Start with
a(1) = 1
-------
Now a(2) is 2 but you are interested in finding the pattern
so you write
a(2) = 2*a(1)
-------
Now a(3) is 4 but you are interested in finding the pattern
so you write
a(3) = 2*a(2) = 2*2*a(1) = 2^2*a(1)
-------
Notice how you try to describe later numbers as related to an earlier number.
----
a(4) = 2^3*a(1)
....
Keep this up as long as you have to till you see a pattern.
a(n) = 2^(n-1)*a(1)
---
Now, a(1) is 1 in this problem so you can drop that
a(n) = 2^(n-1)
========================
Note: A sequence is a function with domain = 1,2,3,4,...,n
You are looking for a Rule for this function.
The Rule has to describe the y-value when n = 1 or 2 or 3, or simply n.
========================
Cheers,
Stan H.
|
|
|
