SOLUTION: Find P if p-3,3p+5 and 18p-5 are three consecutive terms of a geometric progression

Question 1199685: Find P if p-3,3p+5 and 18p-5 are three consecutive terms of a geometric progression
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.


Since the three terms form a geometric progression (GP), you have this equation

     = .


saying that the ratio of the 2nd term to the 1st one is the same as the ratio of the 3rd term to the 2nd
(which is the basic definition of a GP).


To find "p" from this equation, cross-multiply first, and then simplify to get 
a standard form quadratic equation

     = (18p-5)*(p-3)

    9p^2 - 89p - 120 = 0.


Use the quadratic formula to find the solutions to this quadratic equation.


They are p= 10 and p = .


ANSWER.  Possible values of "p" are 10 or .

Solved.

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