(a)	$\begin{align}&\text {2 , 4 , 8} \\[5pt] & \frac{4}{2}=2 , \frac {8}{4} =2\\[5pt] & \frac{4}{2}= \frac {8}{4} =2 \\[5pt] & \underline{\underline{\text{This is a geometric progression with common ratio 2}}}\end{align}$
(b)	$\begin{align}&\text {-6 , -18 , -54} \\[5pt] & \frac{-18}{-6}=3 , \frac {-54}{-18} =3\\[5pt] & \frac{-18}{-6}= \frac {-54}{-18} =3 \\[5pt] & \underline{\underline{\text{This is a geometric progression with common ratio 3}}}\end{align}$
(c)	$\begin{align}&\text {64 , 32 , 16 , 8} \\[5pt] & \frac{32}{64}=\frac{1}{2} , \frac {16}{32} =\frac{1}{2} , \frac{8}{16}=\frac{1}{2}\\[5pt] & \frac{32}{64}= \frac {16}{32} =\frac{8}{16} =\frac{1}{2}\\[5pt] & \underline{\underline{\text{This is a geometric progression with common ratio} \frac{1}{2}}}\end{align}$
(d)	$\begin{align}&\text {5 , 10 , 30 , 120} \\[5pt] & \frac{10}{5}=2 , \frac {30}{10} =3\\[5pt] & \frac{10}{5}\neq \frac {30}{10} \\[5pt] & \underline{\underline{\text{This sequence is not a geometric progression.}}}\end{align}$
(e)	$\begin{align}&\text {-2 , 6 , -18 , 54} \\[5pt] & \frac{6}{-2}=-3 , \frac {-18}{6} =-3 , \frac {54}{-18} = -3\\[5pt] & \frac{6}{-2}=\frac {-18}{6} = \frac {54}{-18} = -3 \\[5pt] & \underline{\underline{\text{This is a geometric progression with common ratio -3}}}\end{align}$
(f)	$\begin{align}&\text {81 , 27 , 3 ,} \frac {1}{9}\\[5pt] & \frac{81}{27}=\frac{1}{3} , \frac {3}{27} =\frac{1}{9}\\[5pt] & \frac{81}{27}\neq \frac {3}{27} \\[5pt] & \underline{\underline{\text{This sequence is not a geometric progression.}}}\end{align}$
(g)	$\begin{align}&\text {0.0002 , 0.002 , 0.02 , 0.2} \\[5pt] & \frac{0.002}{0.0002}=10 , \frac {0.02}{0.002} =10 , \frac {0.2}{0.02} = 10\\[5pt] & \frac{0.002}{0.0002}=\frac {0.02}{0.002} = \frac {0.2}{0.02} = 10 \\[5pt] & \underline{\underline{\text{This is a geometric progression with common ratio 10}}}\end{align}$
(h)	$\begin{align}&\frac {1}{2} , \frac {1}{6} , \frac {1}{18} , \frac {1}{36} . \frac {1}{72}\\[5pt] &\frac {1}{6} \div \frac {1}{2}=\frac{1}{6}\times 2 =\frac{1}{3}\\[5pt] &\frac {1}{18} \div \frac {1}{6}=\frac{1}{18}\times 6 =\frac{1}{3}\\[5pt] &\frac {1}{36} \div \frac {1}{18}=\frac{1}{36}\times 18 =\frac{1}{2}\\[5pt] & \frac {1}{6} \div \frac {1}{2}\neq \frac {1}{36} \div \frac {1}{18} \\[5pt] & \underline{\underline{\text{This sequence is not a geometric progression.}}}\end{align}$

By studying this lesson you will be able to,

Identify whether a given number sequence is a geometric progression.