SOLUTION: find k given the consecutive arithmetic terms: 5, k, k^2-8

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Question 909341: find k given the consecutive arithmetic terms: 5, k, k^2-8
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Given your arithmetic sequence:

k%5E2+-8+-k+=+k+-5 [create quadratic equation = 0 to find k]
k%5E2+-k+-k+-8+%2B5+=+0+
k%5E2+-2k+-3+=+0+ [factor]
k%5E2+%2Bk-3k+-3+=+0+
%28k%5E2+%2Bk%29-%283k+%2B3%29+=+0+
k%28k+%2B1%29-3%28k+%2B1%29+=+0+
%28k+-3%29%28k+%2B1%29+=+0+
so, k+=+3, or k=+-1+