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Question
Show that one of the following progression is a G.P. Also, find the common ratio in case:
−2/3, −6, −54, ...
Solution
We have,
\[ a_1 = \frac{- 2}{3} , a_2 = - 6, a_3 = - 54\]
\[\text { Now }, \frac{a_2}{a_1} = \frac{- 6}{\frac{- 2}{3}} = 9, \frac{a_3}{a_2} = \frac{- 54}{- 6} = 9 \]
\[ \therefore \frac{a_2}{a_1} = \frac{a_3}{a_2} = 9\]
\[\text { Thus, } a_1 , a_2 \text { and } a_3 \text { are in G . P . , where } a = \frac{- 2}{3}\text { and } r = 9 .\]
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