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

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) (Show Source): You can put this solution on YOUR website!
Notice if you divide 4096 by 1024 you get 4 (ie ). Notice how and , etc. So each term is being divided by 4 (or multiplied by ) each time to get the next term. So that means we have a geometric sequence where .

Remember a geometric sequence has the form:

where is the nth term, 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 (we previously solved for this), this means and

Plug in and

So the sequence is

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

Plug in n=0 to find

Evaluate

Simplify. Since n=0 produces (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) (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.
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