Find the next term of the sequence:
$0.1, 0.01, 0.001, 0.0001, . . . . . . . . . .$

0.00001

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0.0001

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0.000001

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0.00000001

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Solution

The correct option is A $0.00001$
Clearly it is a GP with first term $a = 0.1$ and common ratio $r = 0.1$
$t_{n} = a r^{n - 1}$
$t_{5} = 0.1 (0.1)^{4} = 0.00001$ ....Required term
$t_{6} = 0.1 (0.1)^{5} = 0.000001$
$t_{7} = 0.1 (0.1)^{6} = 0.0000001$
$t_{8} = 0.1 (0.1)^{7} = 0.00000001$

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