Find the next term of the sequence:
192, -96, 48, -24, ..........

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Solution

The correct option is A 12
Clearly it is a GP with first term a=192 and common ratio= $\frac{192}{- 96} = \frac{- 1}{2}$
$∴ a_{n} = a r^{n - 1}$
$a_{5} = a r^{4} = 192 (\frac{- 1}{2})^{4} = 192 \times \frac{1}{16} = 12$
$a_{6} = a r^{5} = 192 (\frac{- 1}{2})^{5} = 192 \times \frac{- 1}{32} = - 6$
$a_{7} = a r^{6} = 192 (\frac{- 1}{2})^{6} = 192 \times \frac{1}{64} = 3$
$a_{8} = a r^{7} = 192 (\frac{- 1}{2})^{7} = 192 \times \frac{- 1}{128} = \frac{- 3}{2}$

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