Question 127835
The property of an arithmetic sequence is that if you select a term and from it you subtract
the preceding term, we always get the same answer.
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We are given three terms in the sequence. The first term is y + 8. The second term is 4y + 6.
And the third term is 3y.
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Suppose we choose the second term and subtract from it the preceding (or first) term. In other words we
take 4y + 6 and subtract y + 8. If you do that you get the difference to be 3y - 2.
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Next suppose that we choose the third term 3y and subtract from it the preceding (or 2nd) term
of 4y + 6. When we do that we get a difference of -y - 6.
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But the properties of an arithmetic sequence say that the two differences must be the same.
In an equation we can then set the two differences equal to get:
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3y - 2= -y - 6
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Get rid of the -y on the right side by adding y to both sides to get:
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4y - 2 = -6
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Then get rid of the -2 by adding 2 to both sides to get:
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4y = -4
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Solve this equation by dividing both sides by y to get y = -1
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Take this value for y and substitute it into the original expressions for the three terms
of the arithmetic sequence to find that the terms are:
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First term is y + 8 = -1 + 8 = 7
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Second term is 4y + 6 = 4(-1) + 6 = -4 + 6 = 2
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Third term is 3y = 3(-1) = -3
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Notice the difference between terms is -5. You can then start with the third term and
subtract 5 from it to find that the fourth term is -3 -5 = -8.
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And the fifth term is -13
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and so on ...
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Hope this helps you to understand the problem.
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