To find the formula for the \( n \)th term of the given sequence \(-10, -19, -28, \ldots\), we can start by identifying the pattern in the sequence.
Let's first look at the differences between consecutive terms:
- \(-19 - (-10) = -19 + 10 = -9\)
- \(-28 - (-19) = -28 + 19 = -9\)
The difference between terms is constant at \(-9\). This indicates that the sequence is arithmetic, where the common difference \( d = -9 \).
An arithmetic sequence can be described with the general formula:
\[ a_n = a_1 + (n - 1)d \]
Where:
- \( a_n \) is the \( n \)th term,
- \( a_1 \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term number.
For this sequence:
- The first term \( a_1 = -10 \),
- The common difference \( d = -9 \).
Plugging in these values into the formula gives us:
\[ a_n = -10 + (n - 1)(-9) \] \[ a_n = -10 - 9(n - 1) \] \[ a_n = -10 - 9n + 9 \] \[ a_n = -9n - 1 \]
Thus, the formula for the \( n \)th term of the sequence is:
\[ \boxed{-9n - 1} \]