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()) The unknown numbers below form the start of an arithmetic sequence. \( a, a-b, a-2 b, a-3 b, \ldots \) 4) Which expression represents the common difference between consecutive terms? a-b

Ask by Adkins Bowman. in the United States
Jan 23,2025

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The common difference between consecutive terms is \(-b\).

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In an arithmetic sequence, the common difference between consecutive terms is found by subtracting any term from the term that follows it. In your sequence, the first term is \( a \) and the second term is \( a - b \). So, the common difference is \( (a - b) - a = -b \). This means each term decreases by \( b \), confirming that the sequence steps down in a predictable manner. When working with arithmetic sequences, remember that the common difference remains constant throughout. Mistakes can occur if you try to apply the formula for an arithmetic sequence without clearly defining your terms or miscalculating the difference. Always double-check your calculations when deducing new terms!

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