Subtract the following two equations and solve for $S$ :
$\begin{gathered}
S=a+a x+a x^{2}+a x^{3}+\cdots+a x^{12} \
X S=a x+a x^{2}+a x^{3}+a x^{4}+\cdots+a x^{13}
\end{gathered}$
Assume $x$ is not equal to 1 .
A) $S=\frac{a\left(1-x^{13}\right)}{x}$
B) $ S=\frac{a\left(1-x^{13}\right)}{1-x}$
C) $ S=-a\left(1-x^{13}\right)$
D) $ S=a\left(1-x^{13}\right)$

Question

Quizplus · Accepted Answer

Subtracting the second equation from the first equation, we get:$S-XS=a$$\Rightarrow S(1-x)=a$$\Rightarrow S=\frac{a}{1-x}$$\Rightarrow S=\frac{a\left(1-x^{13}\right)}{1-x}$

Subtract the Following Two Equations and Solve For SSS S=a+ax+ax2+ax3+⋯+ax12XS=ax+ax2+ax3+ax4+⋯+ax13\begin{gathered}S=a+a x+a x^{2}+a x^{3}+\cdots+a x^{12} \\X S=a x+a x^{2}+a x^{3}+a x^{4}+\cdots+a x^{13}\end{gathered}S=a+ax+ax2+ax3+⋯+ax12XS=ax+ax2+ax3+ax4+⋯+ax13​

Subtract the Following Two Equations and Solve For $S$ $\begin{gathered}S=a+a x+a x^{2}+a x^{3}+\cdots+a x^{12} \\X S=a x+a x^{2}+a x^{3}+a x^{4}+\cdots+a x^{13}\end{gathered}$