Math Help - so confusing!

1. so confusing!

hello! I am new! I can post any math homework question I have right?
if this is the case I have one that I don't understand at all!
determine two geometreic sequences whose first terms are 18x-9, 2x+8 and x-1 how would I go about and do this question?

2. Originally Posted by george93
hello! I am new! I can post any math homework question I have right?
if this is the case I have one that I don't understand at all!
determine two geometreic sequences whose first terms are 18x-9, 2x+8 and x-1 how would I go about and do this question?

I presume you are looking for two values of x that would suit?

$a_0 = a_0r^0 = 18x-9$ <-- This defines $a_0$.

$a_1 = a_0r^1 = (18x-9)r = 2x+8$ <-- This defines r.

So $r = \frac{2x+8}{18x-9}$

$a_2 = a_0r^2 = (18x-9) \left ( \frac{2x+8}{18x-9} \right ) ^2 = \frac{(2x+8)^2}{18x-9} = x - 1$ <-- This defines x.

So solve for x:
$\frac{(2x+8)^2}{18x-9} = x - 1$

$(2x+8)^2 = (18x-9)(x-1)$

$4x^2 + 32x + 64 = 18x^2 - 27x + 9$

$0 = 14x^2 - 59x - 55$

Frankly I wouldn't try to fiddle with factoring it, I'd just use the quadratic formula, but as it happens it DOES factor: (which I figured out by using the qf. )
$(14x + 11)(x - 5) = 0$

So x = 5 or x = -11/14.