Question

What is the 17th term in the arithmetic sequence described by this explicit formula?
an =77 +(n-1)(-5)
The 17th term is choose your answer...

Answer 1

To find the 17th term in the arithmetic sequence described by the formula:

\[ a_n = 77 + (n-1)(-5) \]

we substitute \( n = 17 \) into the formula:

\[
a_{17} = 77 + (17 - 1)(-5)
\]

First, calculate \( 17 - 1 \):

\[
17 - 1 = 16
\]

Now substitute this back into the equation:

\[
a_{17} = 77 + 16(-5)
\]

Next, calculate \( 16(-5) \):

\[
16(-5) = -80
\]

Now substitute \(-80\) back into the equation:

\[
a_{17} = 77 - 80
\]

Finally, calculate \( 77 - 80 \):

\[
a_{17} = -3
\]

Therefore, the 17th term is:

\[
\boxed{-3}
\]