Question
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The sequence below is arithmetic. Complete parts (a) through (d) below \( 6,9,12,15, \ldots \) (a) Find the common difference. The common difference is \( d=\square \). (Type a whole number.)

Ask by Mcdonald Wyatt. in the United States
Jan 23,2025

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Answer

The common difference is \( d = 3 \).

Solution

The common difference is \( d = 3 \).

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The common difference of an arithmetic sequence is found by subtracting any term from the term that follows it. In this case, if we take the second term (9) and subtract the first term (6), we get \( 9 - 6 = 3 \). Similarly, looking at the third term (12) and subtracting the second term (9), we also find \( 12 - 9 = 3 \). Thus, the common difference is \( d = 3 \). To double-check, let’s find the common difference between the subsequent terms: \( 15 - 12 = 3 \) confirms our findings. So, the common difference is consistently \( 3 \).

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