9431
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2012-09-18T12:15:34
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Consider the arithmetic sequences $1998, 2005, 2012, ...$ and $1996, 2005, 2014, ...$<br></br>
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Which is the next number after $2005$ that appears in both sequences?<br></br>
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If you liked this problem, <a href="/7016">here is an NRICH task</a> which challenges you to use similar mathematical ideas.<br></br>
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The sequences have common differences of $7$ and $9$ respectively.<br></br>
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The lowest common multiple of $7$ and $9$ is $63$, so the next term after $2005$ to appear in both sequences is $2005 + 63$, that is $2068$.<br></br>
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<mdoxml version="1.0">Patterns and Sequences - Stage 4 Short Problem, UKMT 2005-2006 p83 Q7</mdoxml>
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Weekly Problem 44 - 2012
Consider two arithmetic sequences: 1998, 2005, 2012,... and 1996, 2005, 2014,... Which numbers will appear in both?
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