SOLUTION: If (3-x)+(6)+(7-5x) is a geometric series,find two possible values for a) x b)the common ratio c)the sum of the Gp pls show workings

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Question 1210418: If (3-x)+(6)+(7-5x) is a geometric series,find two possible values for
a) x
b)the common ratio
c)the sum of the Gp
pls show workings
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
If (3-x)+(6)+(7-5x) is a geometric series,find two possible values for
a) x
b)the common ratio
c)the sum of the Gp
pls show workings

Let the common ratio be r

Then


Solve the first equation for r:




Substitute the right side of that for r in the second equation:












5x+3=0; x-5=0
5x=-3;    x=5 
x=-3/5

Substitute x=-3/5 in 




Multiply top and bottom by 5



Substitute x=5 in 






a)x = -3/5 or 5
b)the common ratio = r = 5/3 or r = -3
c)the sum of the GP: 
if x = -3/5               if x = 5
        ditto 
            ditto
                   ditto
              
                 
                 
 
Sum of GP = 98/5  or sum of GP = -14                 

Edwin
Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!


Another tutor has shown one common method for finding the two possible values of x that produce a geometric sequence, and he has then proceeded to answer all the parts of the question.

Here is an alternative method for finding the two possible values of x and hence of the common ratio. (See his response for the remainder of the problem.)

A very useful method for solving many problems involving geometric sequences is using the fact that if A, B, and C are successive terms of the sequence, then



So in this problem,





or
or


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