Question

Find the 9th term of the geometric sequence 4,−16,64,...(1 point) a9 =

Answer 1

To find the 9th term of the geometric sequence given, we first need to identify the first term and the common ratio.

The first term \( a_1 \) is 4.

Next, we need to find the common ratio \( r \). This can be found by dividing the second term by the first term:

\[
r = \frac{-16}{4} = -4
\]

Now that we have the first term \( a_1 = 4 \) and the common ratio \( r = -4 \), we can use the formula for the \( n \)-th term of a geometric sequence:

\[
a_n = a_1 \cdot r^{(n-1)}
\]

To find the 9th term \( a_9 \):

\[
a_9 = a_1 \cdot r^{(9-1)} = 4 \cdot (-4)^{8}
\]

Now we need to calculate \( (-4)^{8} \):

\[
(-4)^{8} = (4^8) = 65536
\]

Now substitute back into the equation for \( a_9 \):

\[
a_9 = 4 \cdot 65536 = 262144
\]

Thus, the 9th term of the geometric sequence is:

\[
\boxed{262144}
\]