What is the 17th term in the arithmetic sequence described by this explicit formula?an = 77 + (n – 1)(–5)A.–3B.162C.157D.–8

1. Break Down the Problem

We need to find the 17th term of the given arithmetic sequence defined by the explicit formula: $a_n = 77 + (n - 1)(-5)$

2. Relevant Concepts

In an arithmetic sequence, the $n$-th term can be calculated using the formula: $a_n = a_1 + (n - 1)d$ where $a_1$ is the first term and $d$ is the common difference. Here, $a_1 = 77$ and $d = -5$.

3. Analysis and Detail

To find the 17th term ($a_{17}$): $a_{17} = 77 + (17 - 1)(-5)$ Calculating the expression step by step:

1. Calculate $17 - 1 = 16$
2. Multiply by the common difference: $16 \times (-5) = -80$
3. Add this result to the first term: $77 + (-80) = 77 - 80 = -3$

4. Verify and Summarize

Now verifying the calculation:

• $16 \times (-5) = -80$ and then $77 - 80 = -3$ confirms that our calculations are correct.

Final Answer

The 17th term in the arithmetic sequence is $-3$.