Answer
$a_1 = \frac{1}{10}$
$a_2 = \frac{1}{100}$
$a_3 = \frac{1}{1000}$
$a_4 = \frac{1}{10000}$
Converges. The limit of the sequence is $0$.
Work Step by Step
$a_{n+1} = \frac{a_n}{10}$; $a_0 = 1$
$a_1 = \frac{a_0}{10} = \frac{1}{10}$
$a_2 = \frac{a_1}{10} = \frac{1}{100}$
$a_3 = \frac{a_2}{10} = \frac{1}{1000}$
$a_4 = \frac{a_3}{10} = \frac{1}{10000}$
Converges and approaches zero. The values of the sequence are decreasing, but given the equation, cannot be negative.
