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:
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Calculate \(77 - 1\): \[ 77 - 1 = 76 \]
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Multiply \(76\) by \(-2\): \[ 76 \cdot (-2) = -152 \]
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Now substitute back into the equation: \[ a_{77} = -17 - 152 \]
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Add the two values: \[ a_{77} = -169 \]
Thus, the 77th term of the sequence is \(\boxed{-169}\).
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