The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r , a, and ar to represent the first three terms, respectively.] The three numbers are _____, _____, and _____.
Accepted Solution
A:
Answer:-1/10, -1/5 , -2/5 or -2/5, -1/5 , -1/10Step-by-step explanation:let a/r, a, ar be the first 3 terms of the geometric seriestheir product would be equal to a^3a^3=-1/125a=-1/5Substitute a=-1/5 into the first 3 terms-1/5r + -1/5+-r/5=-7/10Multiply the terms such that they have a common denominator:-1/5r +-r/5r + -r^2/5r = -3.5r/5rMultiply both sides by 5r-r^2-r-1=-3.5rAdd 3.5r to both sides and multiply the equation by 2-2r^2 + 5r -2=0Factorize the equation(2r-1)(r-2)=0r=0.5 or r-2For the first three terms where r=0.5-2/5, -1/5 , -1/10For the first three terms where r=2-1/10, -1/5 , -2/5