Answer
This is a geometric sequence.
$a_5 = 720$
$a_6 = 1440$
Work Step by Step
To find out if this is an arithmetic sequence, see if there is a common difference between terms:
$90 - 45 = 45$
$180 - 90 = 90$
$360 - 180 = 180$
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:
$\frac{90}{45} = 2$
$\frac{180}{90} = 2$
$\frac{360}{180} = 2$
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 $a_1 = 45$ and $r = 2$.
Set up the equation to find $a_5$:
$a_5 = 45 \bullet 2^{5 - 1}$
Simplify the exponent first:
$a_5 = 45 \bullet 2^{4}$
Evaluate the exponential term:
$a_5 = 45 \bullet 16$
Multiply to solve:
$a_5 = 720$
Set up the equation to find $a_6$:
$a_6 = 45 \bullet 2^{6 - 1}$
Simplify the exponent first:
$a_6 = 45 \bullet 2^{5}$
Evaluate the exponential term:
$a_6 = 45 \bullet 32$
Multiply to solve:
$a_6 = 1440$
