What is the explicit formula for this arithmetic sequence?–11, –18, –25, –32, ...

To find the explicit formula for the given arithmetic sequence, follow these steps:

1. Identify the first term ($a_1$) of the sequence.

   • The first term is $-11$.

2. Determine the common difference ($d$) between consecutive terms.

   • Subtract the first term from the second term: $-18 - (-11) = -18 + 11 = -7$.
   • The common difference is $-7$.

3. Use the general formula for the $n$-th term of an arithmetic sequence: $a_n = a_1 + (n - 1) \cdot d$

4. Substitute the values of $a_1$ and $d$ into the formula: $a_n = -11 + (n - 1) \cdot (-7)$

5. Simplify the expression: $a_n = -11 - 7(n - 1)$ $a_n = -11 - 7n + 7$ $a_n = -7n - 4$

Therefore, the explicit formula for the arithmetic sequence is: $a_n = -7n - 4$