1. Sequences

The terms of some sequences are determined according to the following rule: If the values of a given term t is odd positive integer, then the value next term is 3t-9 if the value of a given term t is an even positive integer then the value next term is 2t-7 if the term of the seuence alternate between two positive integers(a,b,a,b........)what is the sum of two positive integers?

2. Originally Posted by Dragon
The terms of some sequences are determined according to the following rule: If the values of a given term t is odd positive integer, then the value next term is 3t-9 if the value of a given term t is an even positive integer then the value next term is 2t-7 if the term of the seuence alternate between two positive integers(a,b,a,b........)what is the sum of two positive integers?
So you have positive integer $\displaystyle a$ and so the next term is: $\displaystyle 2a-7$

Then the term after that is: $\displaystyle 3(2a-7)-9$

So add a to that: $\displaystyle a+3(2a-7)-9$

Then get rid of parenthesis: $\displaystyle a+6a-21-9$

Add/Subtract: $\displaystyle 7a-30$

And that is as close as you can get.

3. Hello, Dragon!

An interesting problem . . .

The terms of a sequence are determined according to the following rule:
If a term $\displaystyle t$ is odd, then the next term is $\displaystyle 3t-9.$
If a term $\displaystyle t$ is even, then the next term is $\displaystyle 2t-7.$

If the terms of the sequence alternate between two positive integers: a, b, a, b ...
what is the sum of two positive integers?

Let $\displaystyle a$ be an odd positive integer.

Then the next term is: .$\displaystyle b \:=\:3a - 9$ ... an even integer.

Then the next term is: .$\displaystyle c \:=\:2(3a-9) - 7 \:=\:6a - 25$

But this is equal to the first term $\displaystyle a.$
. . Hence, we have: .$\displaystyle 6a - 25\:=\:a\quad\Rightarrow\quad\boxed{a\,=\,5}$

Then: .$\displaystyle b \:=\:3(5) - 9\quad\Rightarrow\quad\boxed{b\:=\:6}$

Thererfore: .$\displaystyle \boxed{a + b \:=\:11}$

4. I thought it said first two even integers Ignore my answer.

Originally Posted by Soroban
But this is equal to the first term $\displaystyle a.$
Why?