SOLUTION: (a) Find x if the numbers 3-x, x, and 1-3x form an arithmetic sequence. And then (b) find the next term of the sequence after the ones represented in part (a).

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Question 141069: (a) Find x if the numbers 3-x, x, and 1-3x form an arithmetic sequence. And then (b) find the next term of the sequence after the ones represented in part (a).
Found 2 solutions by stanbon, vleith:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Find x if the numbers 3-x, x, and 1-3x form an arithmetic sequence. And then
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EQUATIONS:
3-x + d = x
x + d = 1-3x
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Rearrange to get:
2x -d =3
4x +d = 1
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Add to get:
6x = 4
x = 2/3
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2(2/3) - d = 3
(4/3) - 3 = d
d = -5/3
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(b) find the next term of the sequence after the ones represented in part .
next term: 1-3x + d = 1-3x -5/3 = -2/3 - 5x
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Cheers,
Stan H.

Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
In order to be a sequence the difference between each successive pair of terms must be equal.
Thus

Check your answer.
3-x, x, 1-3x
3-2/3 , 2/3 , 1-3(2/3)
7/3 , 2/3 , -3/3
The difference between each term is -5/3.
So the next term is -3/3 - 5/3 = -8/3
-8/3 = y(2/3) --> y = -4
so, in terms of x, then next sequence value is -4x