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62,57,52,47,42,ldots

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62,57,52,47,42,ldots

62,57,52,47,42,ldots

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CharlesElite · Tutor for 8 years

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<p> 37</p>

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<p> This question involves identifying the pattern in a sequence of numbers and predicting the next number(s) in the sequence. The given sequence is 62, 57, 52, 47, 42, ...<br /><br />To find the pattern, we observe the differences between consecutive numbers:<br />- 62 - 57 = 5<br />- 57 - 52 = 5<br />- 52 - 47 = 5<br />- 47 - 42 = 5<br /><br />The difference between each number and the one following it is consistently 5. This indicates that the sequence is an arithmetic sequence where each term is 5 less than the previous term.<br /><br />The formula for the nth term of an arithmetic sequence is given by:<br />\[a_n = a_1 + (n - 1)d\]<br />where \(a_1\) is the first term, \(n\) is the term number, and \(d\) is the common difference between the terms.<br /><br />In this case, \(a_1 = 62\) and \(d = -5\) (since each term is 5 less than the previous one).<br /><br />To find the next term (the 6th term) in the sequence, we set \(n = 6\) and use the formula:<br />\[a_6 = 62 + (6 - 1)(-5)\]</p>
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