How do we get the n th term of the sequence?

[basheer uddin]

Homework Statement

how do we get the n th term of a sequence if it is given in form of
$x_{ n+1 }=f({ x }_{ n })$
and the p th term is given

Homework Equations

I figured we may get it if we get it in the form of
$x_{ n+1 }-{ x }_{ n }$ but how?can we even get it?if yes,under what conditions?

The Attempt at a Solution

example: n th term of sequence where
$x_{ n+1 }=\frac { { x }_{ n }+\frac { 2 }{ { x }_{ n } } }{ 2 }$
where ${ x }_{ 0 }=1$

 

[pasmith]

Non-linear recurrences are unlikely to have solutions in closed form. Iteration is generally the only way to find x_n given x_0.