# Math Help - Find a general formula ...

1. ## Find a general formula ...

Let $x_1 = 1$ and $x_{n+1} = 2x_n + 1, ~ n \geq 1$.

Find and prove a general formula for $x_n$.

Not sure where to start ... Do you solve for $x_n$ ?

2. Originally Posted by jaclyn91
Let $x_1 = 1$ and $x_{n+1} = 2x_n + 1, ~ n \geq 1$.

Find and prove a general formula for $x_n$.

Not sure where to start ... Do you solve for $x_n$ ?
Have you been taught how to solve difference equations (recurrence relations)?

3. Originally Posted by jaclyn91
Let $x_1 = 1$ and $x_{n+1} = 2x_n + 1, ~ n \geq 1$.

Find and prove a general formula for $x_n$.

Not sure where to start ... Do you solve for $x_n$ ?
$x_{n+1}+1=2(x_n+1)\Rightarrow x_{n}+1=2^{n-1}(x_{1}+1)$