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## Homework Statement

The sum of first three numbers of the arithmetic sequence is 54. If you subtract 3 from the first one, leave the second one unchanged and add 12 to the third one you get the first three numbers of the geometric sequence of the form ##ar + ar^2 + ar^3 + ... ar^n ## Find r.

## Homework Equations

3. The Attempt at a Solution [/B]

Using the first clue i got ##a + d = 18 ## ##a ## being the first number in either sequence and ##d ## being the difference of the arithmetic sequence. Next i set up the geometric sequence of the given form ##(a - 3) + (a + d) + (a + 2d + 12) ## . Now ##\frac{a + d}{a - 3} = r ## and from this ##\frac{18}{18 - d} = r ## . Also ##\frac{a + 2d + 12}{a + d} = r^2 ## . Now defining ##18 - \frac{18}{r} = d ## and replacing in the formula above i obtain ##8r - 3 = r^3## . This does not hold for ##r = 2 ## which is the correct solution. Which step did i do wrong?

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