A government program that currently costs taxpayers $$3\mathrm{.}5$ billion per year $is$ cut back $by5\%$ per year.

$(a)$ Write $an$ expression for the amount budgeted $(in$ dollars$)$ for this program after $n$ years.

$A_n=,$ dollars

$(b)$ Compute the budgets for the first $4$ years.

$A_1=$$

$A_2=$$

$A_3=$$

$A_4=$$

$(c)$ Determine the convergence $or$ divergence $of$ the sequence $of$ reduced budgets. $If$ the sequence converges, find its $limit.(If$ the quantity diverges, enter DIVERGES.$)$

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