SOLUTION: Given numbers a,b,c find x: a+x, b+x, c+x are
consecutive in a geometric sequence. What is x?
Algebra.Com
Question 857283: Given numbers a,b,c find x: a+x, b+x, c+x are
consecutive in a geometric sequence. What is x?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
For a+x, b+x, c+x to form a geometric sequence, we must have ^2 = (a+x)(c+x) \Rightarrow x^2 + 2bx + b^2 = x^2 + (a+c)x + ac)
. Subtract x^2 from both sides and you will obtain x \Rightarrow x = \frac{b^2 - ac}{a+c-2b})
, provided this number exists.
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