How would I write this as a recursive formula?

Question

$$400\cdot\left(\dfrac 13\right)^{20}+400\cdot\left(\dfrac 13\right)^{19}+400\cdot\left(\dfrac 13\right)^{18}+400\cdot\left(\dfrac 13\right)^{17}+\cdots+400\cdot \left(\dfrac 13\right)^0.$$

I can solve the problem by doing this manually but I want a sequence formula for this.

Answer 1

(This answer corresponds to the second edition.)

$s_n = s_{n-1} + 400\cdot (\frac13)^{21-n}$ for $n \in \{1,\dots,20\}$, $s_0 = 0$

Answer 2

\begin{eqnarray*} 400 \sum_{i=1}^{21} \left( \frac{1}{3} \right)^{21-i}. \end{eqnarray*}