(repost) Work out the value of x in this arithmetic sequence

[bushra1175]

Hi everyone, I marked my previous post as solved because I thought I figured it out and I'm not sure about how to turn it back. I am royally stuck with a question that seems quite straightforward:

 

[RatherBadAtMath]

I posted a reply that is awaiting approval.

 

[yoscar04]

Hi, do you know the definition of an arithmetic sequence?
Start from there and let's see how it goes.

 

[HallsofIvy]

A sequence \(\displaystyle a_1, a_2, a_3, a_4, ...\) is called an "arithmetic" sequence if and only if \(\displaystyle a_2- a_1= a_3- a_2= a_4- a_3= ...\). That is, that the difference between any two consecutive terms is the same constant. In that case, and calling that common difference "r", the sequence can be written \(\displaystyle a_1, a_1+ r, a_1+ 2r, a_1+ 3r, ...\).

In this case, with three consecutive terms being x, 1/x, and 1 we must have 1/x- x= 1- 1/x. Solve that equation for x.