Question

Use the explicit formula below to find the fifth term of the sequence. Use the Formula Editor x−−√ to type math or use the Image icon to upload a photo of your work.

an=−6(4)n−1

Answer 1

To find the fifth term of the sequence defined by the explicit formula \( a_n = -6(4)^{n-1} \), we need to substitute \( n \) with 5.

Now we calculate \( a_5 \):

\[
a_5 = -6(4)^{5-1} = -6(4)^{4}
\]

Next, we compute \( 4^4 \):

\[
4^4 = 256
\]

Now substitute this back into the equation:

\[
a_5 = -6(256) = -1536
\]

Thus, the fifth term of the sequence is:

\[
\boxed{-1536}
\]