Solution Bank Sequences and Series Target C
Answers to the Practice Problems are below in random order.
\(\begin{align}&1\ & \ \ \ &
a_n=\frac{5}{8}(2)^{n-1}\ & \ \ \ &
(6,0)\ & \ \ \ &
\text{Various derivations}\\\\
&a_n=(2)^{n-1}\ & \ \ \ &
-3.75\ & \ \ \ &
\text{Yes,}\ r=\frac{1}{4}\ & \ \ \ &
\text{About}\ 32\ \text{years}\\\\
&a_n=9(3)^{n-1}\ & \ \ \ &
240\ \text{inches}\ & \ \ \ &
a_n=2^{n-1}\ & \ \ \ &
\text{The series does not converge}\\\\
&a_n=5(\frac{1}{4})^{n-1}\ & \ \ \ &
-\frac{1}{16}\ & \ \ \ &
x=\frac{2}{9}\ & \ \ \ &
\text{Various explanations}\\\\
&a_n=2048(\frac{1}{4})^{n-1}\ & \ \ \ &
\frac{8}{3}\ & \ \ \ &
a_n=6(6)^{n-1}\ & \ \ \ &
\text{No, ratio is not common}\\\\
&a_n=11(4)^{n-1}\ & \ \ \ &
2515.58\ & \ \ \ &
\text{Yes,}\ 15th\ & \ \ \ &
\text{No, arithmetic}\\\\
&a_n=2(-3)^{n-1}\end{align}\)
Answers to the Practice Problems are below in random order.
\(\begin{align}&1\ & \ \ \ &
a_n=\frac{5}{8}(2)^{n-1}\ & \ \ \ &
(6,0)\ & \ \ \ &
\text{Various derivations}\\\\
&a_n=(2)^{n-1}\ & \ \ \ &
-3.75\ & \ \ \ &
\text{Yes,}\ r=\frac{1}{4}\ & \ \ \ &
\text{About}\ 32\ \text{years}\\\\
&a_n=9(3)^{n-1}\ & \ \ \ &
240\ \text{inches}\ & \ \ \ &
a_n=2^{n-1}\ & \ \ \ &
\text{The series does not converge}\\\\
&a_n=5(\frac{1}{4})^{n-1}\ & \ \ \ &
-\frac{1}{16}\ & \ \ \ &
x=\frac{2}{9}\ & \ \ \ &
\text{Various explanations}\\\\
&a_n=2048(\frac{1}{4})^{n-1}\ & \ \ \ &
\frac{8}{3}\ & \ \ \ &
a_n=6(6)^{n-1}\ & \ \ \ &
\text{No, ratio is not common}\\\\
&a_n=11(4)^{n-1}\ & \ \ \ &
2515.58\ & \ \ \ &
\text{Yes,}\ 15th\ & \ \ \ &
\text{No, arithmetic}\\\\
&a_n=2(-3)^{n-1}\end{align}\)