Questions: Answer each question about the following series: 3+4.5+6+7.5+9+10.5. What is the common difference of the arithmetic sequence on which the series is based? d=

Answer each question about the following series: 3+4.5+6+7.5+9+10.5. What is the common difference of the arithmetic sequence on which the series is based? d=
Transcript text: Answer each question about the following series: $3+4.5+6+7.5+9+10.5$. What is the common difference of the arithmetic sequence on which the series is based? \[ d= \]
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Solution

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Solution Steps

To find the common difference of an arithmetic sequence, we need to subtract any term from the previous term in the sequence. The series given is $3, 4.5, 6, 7.5, 9, 10.5$. We can calculate the difference between the first two terms to find the common difference.

Step 1: Identify the Series

The given series is \(3, 4.5, 6, 7.5, 9, 10.5\).

Step 2: Determine the Common Difference

To find the common difference \(d\) of an arithmetic sequence, subtract the first term from the second term: \[ d = 4.5 - 3 = 1.5 \]

Final Answer

The common difference of the arithmetic sequence is \(\boxed{1.5}\).

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