Arithmetic Sequence

[dagr8est]

The first four terms in an arithmetic sequence are x+y, x-y, xy, x/y, in that order. What is the fifth term?
a)-15/8
b)-6/5
c)0
d)27/20
e)123/40

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Let z=difference between terms

x+y+z=x-y
z=-2y

x-y+z=xy
z=xy-x+y

xy+z=x/y
z=(x/y)-xy

I can't figure out how to find the common difference from these results.

 

[Euler]

Could you expand on what you're having trouble on? I don't understand how you have x and y variables, and then you need a numerical answer. On the second problem, if you plug in the values for z, all of the equations you have work out. For instance,

x+y+z=x-y
z=-2y

and you substitute

x+y+(-2y) = x-y

The same goes for the other problems you listed.

 

[dagr8est]

I don't understand how you have x and y variables, and then you need a numerical answer.

I don't know either but that's exactly what the question says so there must be a way to figure out x, y, and the common difference between each term.

On the second problem, if you plug in the values for z, all of the equations you have work out.

I tried that but I didn't get anywhere with it.

 

[tkhunny]

1) z=-2y
2) z=xy-x+y
3) z=(x/y)-xy

You have the right idea. Keep going with it.

1) z = -2y
2) -2y=xy-x+y = x(y-1) + y
3) -2y=(x/y)-xy = x[(1/y) - y] = x[(1-y)/y^2]

1) z = -2y
2) x = -3y/(y-1)
3) -2y= (-3y/(y-1))*[(1-y)/y^2]

Solve 3) for y and you can find x and z.

Find (x/y) + z and you're home.

Hey, I even get one of their answers!