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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?

 Jun 18, 2019
 #1
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+2

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

 Jun 18, 2019
 #7
avatar+208 
0

OMG THX

NoobGuest  Jun 22, 2019
 #2
avatar+8810 
+3

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

 Jun 18, 2019
 #6
avatar+208 
0

OMG THX

NoobGuest  Jun 22, 2019

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