The first four terms of an arithmetic sequence are \( -11,-5 \) What is the equation for \( a_{n} \) ? \( \begin{array}{l}\text { A } a_{n}=-11(n-1)-6 \\ \text { B } a_{n}=6(n-1)-11 \\ \text { C } a_{n}=-11(n-1)+6 \\ \text { D } a_{n}=-6(n-1)-11\end{array} \)

To find the equation for \( a_{n} \) of the arithmetic sequence, we first determine the common difference \( d \). The difference between the second term \( -5 \) and the first term \( -11 \) is: \[ d = -5 - (-11) = -5 + 11 = 6. \] The first term \( a_1 \) is \( -11 \). The general formula for the \( n \)-th term of an arithmetic sequence is: \[ a_n = a_1 + (n-1)d. \] Plugging in our values: \[ a_n = -11 + (n-1) \cdot 6. \] This simplifies to: \[ a_n = -11 + 6n - 6 = 6n - 17. \] And now, let's look at the answer choices: None of the provided options match our derived equation directly. However, the closest representation can be obtained by rewriting \( a_n \) and checking the forms. None are correct in this case. Here's a fun fact: Arithmetic sequences are often used in real-life situations, such as calculating monthly payments or understanding the uniform growth of investments! For a bonus, if you plan on diving deeper into sequences, consider exploring geometric sequences! They're like arithmetic sequences but multiply instead of adding, giving an entirely different spin on the patterns you can create!