SOLUTION: The sum of the second and the third terms of a geometric progression is 6,the sum of the third and the fourth term is -12.find; (a) first

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Question 1055154: The sum of the second and the third terms of a geometric progression is 6,the sum of the third and the fourth term is -12.find;
(a) first term
(b) common ratio
(c) sum of the first 20 terms
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!




So then,


and


I graphed these two equations substituting (x,y) for (a,r) and found an intersection point.


So then,
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
 
The solution above contains an error. He took 

"The sum of the second and the third terms"

as if it were

"The sum of the FIRST and the third terms"

------------------------------------------------

The sum of the second and the third terms of a 
geometric progression is 6,

 




the sum of the third and the fourth term is -12.

 
 

 
 

Set the two expressions for a1 equal:

 

Divide both sides by 6

 

Cross-multiply

 

 

 

Factor out r:

 

Factor the expression in parentheses:

 

Use zero-factor property.  Set each
factor = 0:

 r = 0;  r+1 = 0;  r+2 = 0
          r = -1     r = -2

So we have three potential values for r:

If we use r = 0

Substitute in 

 

 

That's undefined so we must discard r = 0

----

If we use r = -1

Substitute in 

 

 

 

That's also undefined. So we must also discard r = -1

----

If we use r = -2

Substitute in 

 

 

 

    

So the first term is 3,

The sequence = 3, -6, 12, -24, 48, -96, ...

The sum of the first 20 terms:

 

 








Edwin
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