SOLUTION: Your help will be appreciated thanks! Let a(1)=5. Define a(n) to be (a(n-1))/2 if a(n-1) is even, 3a(n-1)+1 if a(n-1) is odd for all other natural numbers n. What is the fourth te

Algebra ->  Sequences-and-series -> SOLUTION: Your help will be appreciated thanks! Let a(1)=5. Define a(n) to be (a(n-1))/2 if a(n-1) is even, 3a(n-1)+1 if a(n-1) is odd for all other natural numbers n. What is the fourth te      Log On


   

Question 1020460: Your help will be appreciated thanks!
Let a(1)=5. Define a(n) to be (a(n-1))/2 if a(n-1) is even, 3a(n-1)+1 if a(n-1) is odd for all other natural numbers n. What is the fourth term of the sequence?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52807) About Me  (Show Source):
You can put this solution on YOUR website!
.
Your help will be appreciated thanks!
Let a(1)=5. Define a(n) to be (a(n-1))/2 if a(n-1) is even, 3a(n-1)+1 if a(n-1) is odd for all other natural numbers n.
What is the fourth term of the sequence?
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Let us calculate the second term. Since a%5B1%5D=5 is odd, a%5B2%5D = 3%2Aa%5B1%5D%2B1 = 3*5+1= 16.

Now calculate the third term. Since a%5B2%5D=16 is even, a%5B3%5D = a%5B2%5D%2F2 = 16%2F2 = 8.

Next calculate the fourth term. Since a%5B3%5D=8 is even, a%5B4%5D = a%5B3%5D%2F2 = 8%2F2 = 4.


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
a.1 = 5

if a.n-1 is even, then a.n = a.n-1 / 2.

if a.n-1 is odd, then a.n = 3 * a.n-1 + 1.

i'm using the convention that a.n is equal to a sub n which is equal to a[n] which is equal to an

we have a.1 = 5.

since a.1 is odd, then a.2 = 3 * a.1 + 1 = 3 * 5 + 1 = 16.

since a.2 is even, then a.3 = a.2 / 2 = 16/2 = 8.

since a.3 is even, then a.4 = a.3 / 2 = 8/4 = 4.

i believe the fourth term is equal to 4, based on this logic.