Question

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

Answer 1

this is a good question, the answer is not obvious to me
takes time maybe
`

Answer 2

In other words, union, just like in history class, is where they all come together in a group. Intersection, just like in a car, is only where they crash.

So as an example, if you are given

Set X: {1, 2, 3, 4, 5, 6}

Set Y: {2, 4, 6, 8, 10 }

X ∪ Y would equal {1, 2, 3, 4, 5, 6, 8, 10 } and X ∩ Ywould equal {2, 4, 6 }.

Answer 3

??

Answer 4

Don't know how to prove it, but try t=5. Seems to work.

Answer 5

i do have an idea
lets call the first term something, say \(a\)
then the next term is \(3a-9\)

Answer 6

which is \(b\)
the term after that is \(a\) again so \[2(3a-9)-7=a\]

Answer 7

which does in fact give you \(a=5\)

Answer 8

don't forget to find \(b\) and add to get your answer

Answer 9

@ospreytriple how did you get it?

Answer 10

Highly technical :) Guess and check.

Answer 11

lol i like guess, more than i like algebra
\[5,6,5,6,...\]