Question 446254
<pre<
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</pre>