Answer
This is a geometric sequence.
$a_5 = 0.125$
$a_6 = 0.0625$
Work Step by Step
To find out if this is an arithmetic sequence, see if there is a common difference between terms:
$1 - 2 = -1$
$0.5 - 1 = -0.5$
$0.25 - 0.5 = -0.25$
There is no common difference; therefore, this is not an arithmetic sequence.
To find if this is a geometric sequence, see if there is a common ratio:
$\frac{1}{2} = 0.5$
$\frac{0.5}{1} = 0.5$
$\frac{0.25}{0.5} = 0.5$
The common ratio is $0.5$; therefore, this is a geometric sequence.
Find the next two terms, $a_5$ and $a_6$, by using the explicit formula for geometric sequences, $a_n = a_1 \bullet r^{n - 1}$. Use $a_1 = 2$ and $r = 0.5$.
Set up the equation to find $a_5$:
$a_5 = 2 \bullet (0.5)^{5 - 1}$
Simplify the exponent first:
$a_5 = 2 \bullet (0.5)^{4}$
Evaluate the exponential term:
$a_5 = 2 \bullet 0.0625$
Multiply to solve:
$a_5 = 0.125$
Set up the equation to find $a_6$:
$a_6 = 2 \bullet (0.5)^{6 - 1}$
Simplify the exponent first:
$a_6 = 2 \bullet (0.5)^{5}$
Evaluate the exponential term:
$a_6 = 2 \bullet (0.03125)$
Multiply to solve:
$a_6 = 0.0625$
