Originally Posted by

**MSUMathStdnt** I feel like I am missing something to this question.

Let $\displaystyle s$ be a real number, $\displaystyle s \ne 0$. Find a sequence $\displaystyle a$ such that $\displaystyle a_n=s \Delta a_n$ and $\displaystyle a_0=1$.

__My answer (so far)__:

$\displaystyle a_n = s \Delta a_n = sa_{n+1}-sa_n\; \Rightarrow\; a_{n+1}=\frac{1+s}{s}a_n$.

Changing indexes:

$\displaystyle a_n=\frac{1+s}{s}a_{n-1}$

$\displaystyle a_0=1$

$\displaystyle a_1=\left( \frac{1+s}{s} \right) \left( 1 \right) = \frac{1+s}{s}$

$\displaystyle a_2=\left( \frac{1+s}{s} \right) \left( 1 \right) = \left( \frac{1+s}{s} \right)^2$

$\displaystyle a_3=\left( \frac{1+s}{s} \right) \left( 1 \right)^2 = \left( \frac{1+s}{s} \right)^3$

$\displaystyle ... $

$\displaystyle \mathbf{a_n= \left( \frac{1+s}{s} \right)^n}$

Is that really all they're looking for?

Thanks.