SOLUTION: true or false. the sequence a(n)=2,4,8,16,32,...is the same as the sequence a(1)=2, a(n)=2a(n-1).

Question 446254: true or false. the sequence a(n)=2,4,8,16,32,...is the same as the sequence a(1)=2, a(n)=2a(n-1).
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
What we need to find out is whether the five things
that are true for
a(n)=2,4,8,16,32,...
are also true for
a(1)=2, a(n)=2a(n-1)
If so the answer is "yes"; otherwise "no".
Below are the five things that are true for
the first that must also be true for the
second in order for the correct answer to
be "true":
A. a(1) = 2
B. a(2) = 4
C. a(3) = 8
D. a(4) = 16
E. a(5) = 32
We are told that
a(1) = 2
So we know that A. is true
Now we will substitute n = 2 to see if B. is true.
a(n)=2a(n-1)
a(2)=2a(2-1)=2a(1)=2*2 = 4
So now we know that B. is true
Now we will substitute n = 3 to see if C. is true.
a(n)=2a(n-1)
a(3)=2a(3-1)=2a(2)=2*4 = 8
So now we know that C. is true
Now we will substitute n = 4 to see if D. is true.
a(n)=2a(n-1)
a(4)=2a(4-1)=2a(3)=2*8 = 16
So now we know that D. is true
Now we will substitute n = 5 to see if E. is true.
a(n)=2a(n-1)
a(5)=2a(5-1)=2a(4)=2*16 = 32
So now we know that E. is true
Since they are all true, the answer is "yes".
Edwin
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