SOLUTION: I am looking for the pattern to these numbers 4096,1024,256,64,?,?,?. I took the subtraction numbers and then divided by three but once I get to 64 I couldn't divide by 3 anymore s

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Question 96064This question is from textbook passport to Algebra &geoemtry
: I am looking for the pattern to these numbers 4096,1024,256,64,?,?,?. I took the subtraction numbers and then divided by three but once I get to 64 I couldn't divide by 3 anymore so what am I doing wrong? This question is from textbook passport to Algebra &geoemtry

Found 2 solutions by jim_thompson5910, checkley71:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Notice if you divide 4096 by 1024 you get 4 (ie 4096%2F1024=4). Notice how 1024%2F256=4 and 256%2F64=4, etc. So each term is being divided by 4 (or multiplied by 1%2F4) each time to get the next term. So that means we have a geometric sequence where r=1%2F4.

Remember a geometric sequence has the form:

a%5Bn%5D=a%5B1%5D%28r%29%5En where a%5Bn%5D is the nth term, a%5B1%5D is the first term, and r is the ratio between the terms. note: n starts at zero.

Since the first term is 4096, and the ratio is 1%2F4 (we previously solved for this), this means a%5B1%5D=4096 and r=1%2F4


a%5Bn%5D=4096%281%2F4%29%5En Plug in a%5B1%5D=4096 and r=1%2F4


So the sequence is a%5Bn%5D=4096%281%2F4%29%5En


You can check this answer by plugging in n=0 to get 4096

a%5Bn%5D=4096%281%2F4%29%5E0Plug in n=0 to find a%5Bn%5D


a%5Bn%5D=4096%281%29 Evaluate %281%2F4%29%5E0

a%5Bn%5D=4096 Simplify. Since n=0 produces a%5Bn%5D=4096 (our first number in the sequence), this partly verifies our sequence.


And you can do this for every value of n to fully verify your answer.

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
4096/4=1024/4=256/4=64/4=16/4=4/4=1 1/4 is the factor not 1/3.