Asked by Lara

I NEED URGENT HELP WITH THIS QUESTION!!!!

Question:

The terms of a geometric sequence are 4x+1, x+4, and 10-x. Determine the value of x.
Answered by oobleck
since there is a common ratio between terms,
(x+4)/(4x+1) = (10-x)/(x+4)
Now just solve for x.
Answered by Reiny
Use your definition.

(x+4)/(4x+1) = (10-x)/(x+4)
(x+4)^2 = (4x+1)(10-x)
x^2 + 8x + 16 = 40x - 4x^2 + 10 - x
5x^2 - 31x + 6 = 0
solve for x, it factors
Answered by Lara
Did that and it didn’t work. I am not getting the correct value for x. x = 6.


It would be great if someone showed me the steps on how to solve the question
Answered by Reiny
I told you it factored
5x^2 - 31x + 6 = 0
(x-6)(5x-1) = 0
x = 6 or x = 1/5

if x = 6, your terms are: 25, 10, and 4
notice 10/25 = 4/10 = 2/5

if x = 1/5, your terms are : 9/5, 21/5, and 49/5
is (21/5) ÷ (9/5) = (49/5) ÷ (21/5) ??

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