The terms of a particular sequence are determined according to the following rules:
* If the value of a given term is an odd positive integer s, then the value of the following term is 3s  9
* If the value of a given term is an even positive integer t, then the value of the following term is 2t  7.
Suppose that the terms of the sequence alternate between two positive integers (a,b,a,b,...).
What is the sum of the two positive integers?
Here is one possibility:
First term =5
Second term =3*5  9 =6
Second term =6
Third term =2*6  7 =5
Third term =5
Fourth term =3*5  9 =6
So, the sequence alternates as follows:
5, 6, 5, 6, 5, 6..........and so on:
Sum =5 + 6 = 11
Let's say a is the odd one and b is the even one. Then we can say...
a = 2b  7 and b = 3a  9
So we can substitute 3a  9 in for b to find a:  
a = 2b  7 

a = 2(3a  9)  7 

a = 6a  18  7 

a = 6a  25 

5a = 25 

a = 5 

Now we can substitute 5 in for a to find b: 

b = 3a  9 

b = 3(5)  9  
b = 15  9 

b = 6 
And...
a + b = 5 + 6 = 11