# Thread: find x if the numbes 3-x, x, and 1-3x form an arithmetic sequence.

1. ## find x if the numbes 3-x, x, and 1-3x form an arithmetic sequence.

find x if the numbes 3-x, x, and 1-3x form an arithmetic sequence. find the next term in the sequence
could you guys help me on how to solve this? my teacher gave me a vague explanation but i dont understand

2. I can infer from context that you've not shown any work because you're stuck at the very beginning and have none to show. That's perfectly alright. The key words to pick out of the problem text are arithmetic sequence (you might have seen it called an arithmetic progression). This gives you a good topic to search your class notes, textbook, and any handouts you may have been given for a refresher on this topic. If you're finding all of those insufficient, you might also try this page from Math is Fun.

With that in mind, in order for the three given numbers to form an arithmetic sequence, there needs be some common difference. What expression, in terms of x, do you need to add to 3 - x to get x? What happens if you then add this same difference again to x? Using what you know about arithmetic sequences, what expression must this be equal to? Where does this all lead you? Go ahead and give the problem your best effort. If you get stuck again, that's fine, but when you reply back please include any and all work you've done on the problem, even including the parts you know for sure are wrong. Thank you.

3. Originally Posted by ksdhart2
I can infer from context that you've not shown any work because you're stuck at the very beginning and have none to show. That's perfectly alright. The key words to pick out of the problem text are arithmetic sequence (you might have seen it called an arithmetic progression). This gives you a good topic to search your class notes, textbook, and any handouts you may have been given for a refresher on this topic. If you're finding all of those insufficient, you might also try this page from Math is Fun.

With that in mind, in order for the three given numbers to form an arithmetic sequence, there needs be some common difference. What expression, in terms of x, do you need to add to 3 - x to get x? What happens if you then add this same difference again to x? Using what you know about arithmetic sequences, what expression must this be equal to? Where does this all lead you? Go ahead and give the problem your best effort. If you get stuck again, that's fine, but when you reply back please include any and all work you've done on the problem, even including the parts you know for sure are wrong. Thank you.
thanks for giving me a vague explanation too, i've already figured it out but thanks for your "help." i solved it for x=2/3 and then plugged in x.

4. Originally Posted by hamburgerman1212
thanks for giving me a vague explanation too, i've already figured it out but thanks for your "help." i solved it for x=2/3 and then plugged in x.
Hey man, don't give the people here attitude. This site exists to help people learn math, not to do their homework for them. We already know how to do algebra. You don't learn anything if we just give you the answer. You're also not entitled to be spoonfed a solution.

The "vague explanation" given by ksdhart2 was actually detailed, clear, cheerful, and it contained all of the concepts and info you needed to solve this problem. He/she even led you through the steps of the solution by posing the specific questions that you needed to investigate. E.g. "What expression, in terms of x, do you need to add to 3 - x to get x?". Did you even read that part? Did you answer that question? If you solved the problem, then you must have. You could always have followed up with another post here (with the specific steps you attempted) if you followed ksdhart2's advice and still got stuck. In any case your goal isn't only to get the answer to this specific question. It's to learn what arithmetic sequences are and how to do algebraic manipulations. Do you know how to do that? What are you going to do when it's a different problem, on a test, and you can't demand a solution on an online forum?

5. Originally Posted by Denis
There was no need to solve for x.
This simple:
d = difference between 1st 2 terms
4th term = 3rd term + d
Actually, Denis, the problem text specifically instructed OP to "find x," directly implying that they were meant to come up with a numerical solution rather than an expression in x.

6. hamburgerman1212,

let d = the common difference.

3 - x + d = x
x + d = 1 - 3x
----------------

2x - d = 3
4x + d = 1
-------------

Part (i) Continue solving for x.

Part (ii) Solve for the 4th arithmetic term.

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