Given that x, 4, x+6 are consecutive terms of a geometric series, find:
(a) the possible values of x
So I got x=2 but part from trying every number to see I don't know of a method to find the possible values. I don't know how many values they want so if there is a method that shows all the possible values that would be better.

Question

Given that x, 4, x+6 are consecutive terms of a geometric series, find:
(a) the possible values of x
So I got x=2 but part from trying every number to see I don't know of a method to find the possible values. I don't know how many values they want so if there is a method that shows all the possible values that would be better.

welshfella · Answer

Geometric series so  common ratio = second term / first = third / second

so    4 / x = (x + 6) / 4

solve for x

welshfella · Answer

that rearranges to the quadrataic equation

x^2 + 6x - 16 = 0

welshfella · Answer

can you solve that?

welshfella · Answer

x = 2 is one of the possible values

welshfella · Answer

you need to factor 
x^2 + 6x - 16

you want 2 numbers whose product is -16 and whose sum = + 6

welshfella · Answer

have you learned how to solve these type of equations?

anonymous · Answer

Yes I have done quadratics before. I will try that now quickly

anonymous · Answer

I got the right thing! Thank you very much!

welshfella · Answer

yw