<u>Answer:</u>
<u><em>41</em></u>
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<u>Explanation:</u>
To solve this problem we must first understand what the pattern is in the arithmetic sequence. Once we understand the pattern, we can then apply it to the final known term to find the next term.
Take a look at the arithmetic sequence given:
<em>9, 17, 25, 33,...</em>
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Let's start by figuring out how they got the second term in the sequence. To do that, subtract the second term by the first term. This will reveal the pattern.
<em>9 - first term</em>
<em>17 - second term</em>
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<em>17 - 9 = 8</em>
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So, this means they added eight to get the next term. Therefore, the pattern should be 'add eight' to get the next term. Just to be sure the pattern we found is correct, apply it to the given arithmetic sequence.
<em>9, 17, 25, 33,...</em>
<em>9 </em><em>+ 8 = </em><em>17</em>
<em>17 </em><em>+ 8 = </em><em>25</em>
<em>25 </em><em>+ 8 = </em><em>33</em>
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So, since 'adding eight' every time gives us the next term, the pattern is correct.
Finally, let's continue the pattern to find the next term.
<em>9, 17, 25, 33,...</em>
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<em>33 </em><em>+ 8 = </em><em>41</em>
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<em>9, 17, 25, 33, 41,...</em>
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Therefore, the next term in the arithmetic sequence is <u><em>41</em></u>.
