I have written a program to do the following:

Initialize P$(1)$ with $5.$

Define a FOR loop that uses loop variable t to iterate through values $1$ to $5$ at a step of $1.$

In each iteration of the FOR loop, assign P$($t $+1)$ with P$($t$)+0\mathrm{.}0625*$ P$($t$).$

Output the vector P after the FOR loop.

Output the length of the vector using length$($P$).$

Can you tell me the high$-$level purpose of this program?

What can I use it for?

Can this problem be solved without using a loop?