SOLUTION: if (3-x)+(6)+(7-5x) is a geometric series, find the two possible values for x, the common ratio and the sum of GP

Algebra ->  Sequences-and-series -> SOLUTION: if (3-x)+(6)+(7-5x) is a geometric series, find the two possible values for x, the common ratio and the sum of GP      Log On


   

Question 1005957: if (3-x)+(6)+(7-5x) is a geometric series, find the two possible values for x, the common ratio and the sum of GP
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The three TERMS for the series are shown.
Successive ratios must be equal.

highlight_green%28%287-5x%29%2F6=6%2F%283-x%29%29, the successive ratios
%287-5x%29%283-x%29=36
21-15x-7x%2B5x%5E2-36=0
5x%5E2-22x%2B21-36=0
5x%5E2-22x-15=0

General solution formula for a quadratic equation gives
x=%2822%2B-+sqrt%2822%5E2-4%2A5%2A%28-15%29%29%29%2F%282%2A5%29
x=%2822%2B-+sqrt%2822%5E2%2B20%2A15%29%29%2F%282%2A5%29
x=%2822%2B-+sqrt%28784%29%29%2F10
x=%2822%2B-+28%29%2F10
x=%2811%2B-+14%29%2F5
highlight%28x=-3%2F5%29 OR highlight%28x=5%29