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Home » Show that each one of the following progressions is a G.P. Also, find the common ratio in each case: (i) (ii)
Show that each one of the following progressions is a G.P. Also, find the common ratio in each case:
(i) 4,-2,1,-1 / 2, \ldots
(ii) -2 / 3,-6,-54, \ldots .
CBSE | Class 11 | Exercise 20.1 | Geometric Progressions | Maths | RD Sharma
Show that each one of the following progressions is a G.P. Also, find the common ratio in each case:
(i) 4,-2,1,-1 / 2, \ldots
(ii) -2 / 3,-6,-54, \ldots .

Solution:

(i) 4,-2,1,-1 / 2, \ldots
Let a=4, b=-2, c=1
In \mathrm{GP}
\begin{array}{l} b^{2}=a c \\ (-2)^{2}=4(1) \\ 4=4 \end{array}
Therefore, the Common ratio =r=-2 / 4=-1 / 2

(ii) -2 / 3,-6,-54, \ldots
Let a=-2 / 3, b=-6, c=-54
In Geometric Progression
\begin{array}{l} b^{2}=a c \\ (-6)^{2}=-2 / 3 \times(-54) \\ 36=36 \end{array}
Therefore, the Common ratio =r=-6 /(-2 / 3)=-6 \times 3 /-2=9

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