This problem involves the following sequence

$(1)=0$

$()=(1)+3(7)$

$3\mathrm{.}1(10$ points$)$ Solve $()$ using the first$-$order linear equation formula

$3\mathrm{.}2(8$ points$)$ The following program calculates $().$ Please fill in the invariant and the intermediate steps

needed to prove the function returns the formula you calculated in $3\mathrm{.}1$