\begin{tabular}{|l|l|} Write the arithmetic sequence \( -14,-11,-8,-5, \ldots \) in the standard form: \\ \( a_{n}=\square \) Preview \end{tabular}\( | \)

To write the arithmetic sequence \( -14, -11, -8, -5, \ldots \) in standard form, we first need to identify the first term and the common difference. 1. **First term (\( a_1 \))**: The first term of the sequence is \( -14 \). 2. **Common difference (\( d \))**: To find the common difference, we subtract the first term from the second term: \[ d = -11 - (-14) = -11 + 14 = 3 \] Now that we have the first term and the common difference, we can write the general term of the arithmetic sequence in standard form. The formula for the \( n \)-th term of an arithmetic sequence is given by: \[ a_n = a_1 + (n - 1) \cdot d \] Substituting the values we found: - \( a_1 = -14 \) - \( d = 3 \) The formula becomes: \[ a_n = -14 + (n - 1) \cdot 3 \] Now, we can simplify this expression: \[ a_n = -14 + 3(n - 1) \] \[ a_n = -14 + 3n - 3 \] \[ a_n = 3n - 17 \] Thus, the standard form of the arithmetic sequence is: \[ a_n = 3n - 17 \]