Irite variable expressions for arithmetic sequences 5 VF Vrite an expression to describe the sequence below. Use \( n \) to represent n the sequence, where \( n=1 \) for the first term. \( -7,-6,-5,-4, \ldots \) \( a_{n}=\square \) Submit Work it out

To find a variable expression for the given arithmetic sequence: \[ -7, -6, -5, -4, \ldots \] we'll follow these steps: ### 1. Identify the First Term (\(a_1\)) and the Common Difference (\(d\)): - **First term (\(a_1\))**: This is the first number in the sequence. \[ a_1 = -7 \] - **Common difference (\(d\))**: This is the difference between consecutive terms. \[ d = (-6) - (-7) = 1 \] ### 2. Use the Arithmetic Sequence Formula: The general formula for the \(n\)-th term of an arithmetic sequence is: \[ a_n = a_1 + (n - 1) \times d \] Plugging in the values we found: \[ a_n = -7 + (n - 1) \times 1 \] ### 3. Simplify the Expression: \[ a_n = -7 + n - 1 = n - 8 \] ### 4. Final Expression: \[ a_n = n - 8 \] **Verification:** Let's check if this formula works for the first few terms. - **For \(n = 1\):** \[ a_1 = 1 - 8 = -7 \quad \text{(matches the first term)} \] - **For \(n = 2\):** \[ a_2 = 2 - 8 = -6 \quad \text{(matches the second term)} \] - **For \(n = 3\):** \[ a_3 = 3 - 8 = -5 \quad \text{(matches the third term)} \] - **For \(n = 4\):** \[ a_4 = 4 - 8 = -4 \quad \text{(matches the fourth term)} \] Since the formula correctly generates the terms of the sequence, our expression is correct. \[ \boxed{a_n = n - 8} \]