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Definition: A(3)=3-8n What is A(11)-A(...

Definition: `A_(3)=3-8n`
What is `A_(11)-A_(9)`?

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To solve the problem, we need to find the values of \( A_{11} \) and \( A_{9} \) using the given formula \( A_n = 3 - 8n \), and then calculate \( A_{11} - A_{9} \). ### Step-by-step Solution: 1. **Find \( A_{11} \)**: - Substitute \( n = 11 \) into the formula: \[ A_{11} = 3 - 8 \times 11 \] - Calculate \( 8 \times 11 \): \[ 8 \times 11 = 88 \] - Now substitute back: \[ A_{11} = 3 - 88 \] - Perform the subtraction: \[ A_{11} = -85 \] 2. **Find \( A_{9} \)**: - Substitute \( n = 9 \) into the formula: \[ A_{9} = 3 - 8 \times 9 \] - Calculate \( 8 \times 9 \): \[ 8 \times 9 = 72 \] - Now substitute back: \[ A_{9} = 3 - 72 \] - Perform the subtraction: \[ A_{9} = -69 \] 3. **Calculate \( A_{11} - A_{9} \)**: - Substitute the values we found: \[ A_{11} - A_{9} = -85 - (-69) \] - Simplify the expression: \[ A_{11} - A_{9} = -85 + 69 \] - Perform the addition: \[ A_{11} - A_{9} = -16 \] ### Final Answer: \[ A_{11} - A_{9} = -16 \]
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