Question

-17-2 77th term

Answer 1

To find the 77th term of the arithmetic sequence that starts with -17 and has a common difference of -2, we use the formula for the \(n\)-th term of an arithmetic sequence:

\[
a_n = a_1 + (n - 1) \cdot d
\]

Where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.

Given:
- \(a_1 = -17\),
- \(d = -2\),
- \(n = 77\).

Now we plug in the values:

\[
a_{77} = -17 + (77 - 1) \cdot (-2)
\]

Calculating the values step-by-step:

1. Calculate \(77 - 1\):
\[
77 - 1 = 76
\]

2. Multiply \(76\) by \(-2\):
\[
76 \cdot (-2) = -152
\]

3. Now substitute back into the equation:
\[
a_{77} = -17 - 152
\]

4. Add the two values:
\[
a_{77} = -169
\]

Thus, the 77th term of the sequence is \(\boxed{-169}\).