Answer
This is a geometric sequence.
$a_5 = 3$
$a_6 = -3$
Work Step by Step
To find out if this is an arithmetic sequence, see if there is a common difference between terms:
$-3 - 3 = -6$
$3 - (-3) = 0$
$-3 - 3 = -6$
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:
$\frac{-3}{3} = -1$
$\frac{3}{-3} = -1$
$\frac{-3}{3} = -1$
The common ratio is $-1$; 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 $a_1 = 3$ and $r = -1$.
Set up the equation to find $a_5$:
$a_5 = 3 \bullet (-1)^{5 - 1}$
Simplify the exponent first:
$a_5 = 3 \bullet (-1)^{4}$
Evaluate the exponential term:
$a_5 = 3 \bullet (1)$
Multiply to solve:
$a_5 = 3$
Set up the equation to find $a_6$:
$a_6 = 3 \bullet (-1)^{6 - 1}$
Simplify the exponent first:
$a_6 = 3 \bullet (-1)^{5}$
Evaluate the exponential term:
$a_6 = 3 \bullet (-1)$
Multiply to solve:
$a_6 = -3$
