+209 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
+9466 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
