The 5th term in a geometric sequence is 160. The seventh term is 40. What are the possible values for the sixth term?

I think it's 80? Half of 160 is 80, and half of 80 is 40..?

Question

The 5th term in a geometric sequence is 160.  The seventh term is 40.  What are the possible values for the sixth term?

I think it's 80?  Half of 160 is 80, and half of 80 is 40..?

anonymous · Answer

The sequence is decreasing. Let sixth term be X. So you Have 160, X, 40
Introduce another variable k as the common multiple.
So X=k(160) and 40=k(X)
Single out k for both equations and equate

anonymous · Answer

80's right

anonymous · Answer

Can you help me with more?

anonymous · Answer

yup

anonymous · Answer

Great, it'll take me a moment to find one I need help with.

anonymous · Answer

What is the equation of a parabola with the vertex at the origin and focus (-5,0)

anonymous · Answer

@ArsalanAijaz

anonymous · Answer

parabola or hyperbola?

anonymous · Answer

Parabola

anonymous · Answer

It should be something like this.. But I dont know :(
$$y=ax ^{2}+bx$$

anonymous · Answer

That's okay.  can you write an equation for the translation of y=6/x that has the asymptotes x=4 and y=5?

anonymous · Answer

$$y=6\div(x-4)$$
I'm forgetting what to do with the horizontal asymptote :(

anonymous · Answer

I think it's $$y=\frac{ 6 }{ x-4 }+5$$

triciaal · Answer

regarding the original question 
the choices  means more than one
the answer would be 80 and negative 80
the common ratio can be 1/2 or -1/2 
the nth term in a geometric progression is given by a1*r^n-1 where a1 is the first term simplified we get a7/a6 = a6/a5
a7*a5 = a6^2  when you take the square root you always have a positive and a negative

triciaal · Answer

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