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B(n)=(-1)^(n)xxn+3 for all integers n ge...

`B_(n)=(-1)^(n)xxn+3` for all integers `n ge1`. What is the 9th term of the sequence?

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To find the 9th term of the sequence defined by the formula \( B_n = (-1)^n \cdot n + 3 \) for all integers \( n \geq 1 \), we will follow these steps: ### Step 1: Identify the formula The formula for the nth term of the sequence is given as: \[ B_n = (-1)^n \cdot n + 3 \] ### Step 2: Substitute \( n = 9 \) To find the 9th term, we substitute \( n = 9 \) into the formula: \[ B_9 = (-1)^9 \cdot 9 + 3 \] ### Step 3: Calculate \( (-1)^9 \) Since 9 is an odd number, we know that: \[ (-1)^9 = -1 \] ### Step 4: Substitute back into the equation Now substituting \( (-1)^9 \) back into the equation: \[ B_9 = -1 \cdot 9 + 3 \] ### Step 5: Perform the multiplication Calculating the multiplication: \[ B_9 = -9 + 3 \] ### Step 6: Perform the addition Now, we add: \[ B_9 = -9 + 3 = -6 \] ### Final Answer Thus, the 9th term of the sequence is: \[ \boxed{-6} \] ---
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