Answer
This is a geometric sequence.
$a_5 = -80$
$a_6 = 160$
Work Step by Step
To find out if this is an arithmetic sequence, see if there is a common difference between terms:
$10 - (-5) = 15$
$-20 - 10 = -30$
$40 - (-20) = 60$
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:
$\frac{10}{-5} = -2$
$\frac{-20}{10} = -2$
$\frac{40}{-20} = -2$
The common ratio is $-2$; 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 $a_1 = -5$ and $r = -2$.
Set up the equation to find $a_5$:
$a_5 = -5 \bullet (-2)^{5 - 1}$
Simplify the exponent first:
$a_5 = -5 \bullet (-2)^{4}$
Evaluate the exponential term:
$a_5 = -5 \bullet 16$
Multiply to solve:
$a_5 = -80$
Set up the equation to find $a_6$:
$a_6 = -5 \bullet (-2)^{6 - 1}$
Simplify the exponent first:
$a_6 = -5 \bullet (-2)^{5}$
Evaluate the exponential term:
$a_6 = -5 \bullet (-32)$
Multiply to solve:
$a_6 = 160$
