Sequences?

[ChristaJoy]

Not sure if this is the right message board, but it's right out of my "unit circle approach to trigonometry," so here it is!

Find x so that x-1, x, and x+2 are consecutive terms.

Normally I can look at examples from the book and understand the process of how to solve these problems, but there is nothing like this in my book and I can't find out the first couple steps. Any help would be greatly appreciated Thank you!

 

[MarkFL]

Is that the entire problem? No other information is given?

 

[Deleted member 4993]

Not sure if this is the right message board, but it's right out of my "unit circle approach to trigonometry," so here it is!

Find x so that x-1, x, and x+2 are consecutive terms.

Normally I can look at examples from the book and understand the process of how to solve these problems, but there is nothing like this in my book and I can't find out the first couple steps. Any help would be greatly appreciated Thank you!

Please explain - what is x?

 

[soroban]

Hello, ChristaJoy!

I think I know what you meant to say . . .

Find \(\displaystyle x\) so that \(\displaystyle x-1,\,x,\,x+2\) are consecutive terms [COLOR=#b000e]of a geometric sequence.[/COLOR]

We have: .\(\displaystyle \begin{Bmatrix}r &=& \dfrac{x}{x-1} & [1] \\ r &=& \dfrac{x+2}{x} & [2] \end{Bmatrix}\)


Equate [1] and [2]: .\(\displaystyle \dfrac{x}{x-1} \:=\:\dfrac{x+2}{x} \quad\Rightarrow\quad x^2 \:=\: x^2+x-2 \)


Therefore: .\(\displaystyle x \:=\:2\)

 

[HallsofIvy]

x is the mark used by teachers to indicate your answer is wrong...
it is also used, usually in triplicate, to tell you not to go see certain movies...

Gosh, I always thought they meant you should see them!

 

[Deleted member 4993]

Gosh, I always thought they meant you should see them! (for ages 18 - 60)

Denis is carded and can't get in there!!!

 

[HallsofIvy]

Not sure if this is the right message board, but it's right out of my "unit circle approach to trigonometry," so here it is!

Find x so that x-1, x, and x+2 are consecutive terms.

I was going to ask "consecutive terms" of what and point out that there are many different kinds of sequences, in particular both arithmetic and geometric sequences. But I think that Soroban has it right, that this is a geometric sequence because this a "geometric" problem! "Geometric sequences" are so called because if you drop a perpendicular from the right angle of a right triangle to the hypotenuse, you divide the hypotenuse into two intervals of lengths a and c, that, together with the length, b, of the altitude, form a geometric series, a, b, c.
Normally I can look at examples from the book and understand the process of how to solve these problems, but there is nothing like this in my book and I can't find out the first couple steps. Any help would be greatly appreciated Thank you![/QUOTE]