A finite geometric series of $n$ terms is given by $y_n=1+x+x^2+x^3+$dots$+x^{n-1},$ where It is well known that when $n=,y_{}=\frac{1}{1-x}.$

$($a$)$ Write a For Loop$-$based program called Finite Geometric Series that, given $n$ and $x$ as inputs via front$-$panel Numeric Controls, determines $y_n,$ calculates its percentage deviation from $y_{},$ and displays these two results in Numeric Indicators. You may find Add Array Elements in Functions $>$ Programming $>$ Numericas wellasiconsintheFunctions $>$ Programming $>$ Mathematics $$ Elementary & Special Functions $>$ Exponential Functions subpalette useful.

$($b$)$ Use your VI to answer the following question: If $x=0\mathrm{.}5$ and one wishes $y_n$ to deviate from $y_{}=2\mathrm{.}000$dots by less than $0\mathrm{.}1\%,$ what is the minimum required value of $n?$