Let's say I have a sequence $\{x_1,...x_n\}\in\mathbb{R}^+$, where $x_i
Is it possible to form a new sequence $z_m$ by inserting values $y_k$ in between the $x_n$ as necessary (for e.g., ${x_1,y_1,y_2,x_2,y_3,...y_k,x_n}$) such that $z_{i+1}-z_i=c$, a constant?
Are there cases where this can/cannot be done? How does one prove if it is/is not possible?
Lastly, I really don't know what tags to assign, so hope someone helps me out here.