Question 1 and 2, Exercise 4.4
Solutions of Question 1 and 2 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.
Question 1
Determine whether each sequence is geometric. If so, find the common ratio. $5,20,100,500, \ldots$
Solution.
Given sequence is $5, 20, 100, 500, \ldots $.
A sequence is geometric if any two of its consecutive terms have same ratio. Here
\begin{align*}
\frac{20}{5} = 4\neq \frac{100}{20} = 5.\end{align*}
Hence given sequence is not geometric. 
Alternative Method
Given sequence is $5, 20, 100, 500, \ldots $.
Suppose
\begin{align*}
r_1& =\frac{20}{5} = 4\\
r_2&=\frac{100}{20} = 5\\
r_3&=\frac{500}{100} = 5.
\end{align*}
Since $r_1 \neq r_2$, it means two consective terms has different ratio.
Hence given sequence is not geometric.
Question 2
Determine whether each sequence is geometric. If so, find the common ratio. $2,4,6,8, \ldots$
Solution.
Given sequence is \(2, 4, 6, 8, \ldots\).
Suppose
\begin{align*}
r_1&=\frac{4}{2} = 2 \\
r_2&=\frac{6}{4} = \frac{3}{2} \\
r_3&=\frac{8}{6} =\frac{4}{3}
\end{align*}
Since $r_1 \neq r_2 \neq r_3$, it means two consecutive terms has different ratio.
Hence given sequence is not geometric.
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