SOLUTION: For the given geometric sequence tₓ find r if S₂=10 and S₄=50

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Question 1123877: For the given geometric sequence tₓ find r if S₂=10 and S₄=50
Found 3 solutions by greenestamps, ikleyn, MathTherapy:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


S(4) = S(2)*r^2

So

50 = 10r^2
r^2 = 5

r can be either sqrt(5) or -sqrt(5)
Answer by ikleyn(52847)   (Show Source): You can put this solution on YOUR website!
.
From the post, I hardly can read the small symbol " t " with subscript " x " and have no idea what does it mean.


But I guess, and my guessing is that    is the sum of the first 2 terms of some geometric progression, 
while    is the sum  of the first 4 terms of the same geometric progression.


If so, then this info can be presented as these two equations


a + ar = 10,                      (1)

a + ar + ar^2 + ar^3 = 50         (2)


and the problem is to find the common ratio "r" from these equations.


We can rewrite equation (2) in the form

(a+ar) + r^2*(a+ar) = 50.


Replacing  (a+ar)  by 10  in this equation, based on (1), gives

10 + 10r^2 = 50,


which implies  r^2 =  =  = 4  


and then  r = +/-  = +/- 2.


Answer.  The common ratio r may have two values: 2 or -2.

Solved.

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

Notice.   It is possible to make one step further and to determine the first term "a" of the progression.

              But since the problem does not ask to do it,  I stop at this point.



Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

For the given geometric sequence tₓ find r if S₂=10 and S₄=50


IGNORE all other NON-SIMILAR answers! 

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