document.write( "Question 404050: consider the following infinite sequence of numbers 17, 24, 31, 38, 45, 52. what is the least term in the sequence that is a multiple of 2, 3, 4, 5, 6? \n" ); document.write( "

Algebra.Com's Answer #285621 by richard1234(7193) $\"\"$ $\"About$

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We want the least term that is a multiple of the LCM of 2, 3, ..., 6, or 60.\r
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\n" ); document.write( "\n" ); document.write( "Our sequence is denoted by 17 + 7k, where k is an integer. Writing everything modulo 2, 3, and 5, we obtain\r
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\n" ); document.write( "\n" ); document.write( "1 + k ≡ 0 (mod 2) --> k ≡ 1 (mod 2)
\n" ); document.write( "2 + k ≡ 0 (mod 3) --> k ≡ 1 (mod 3)
\n" ); document.write( "2 + 2k ≡ 0 (mod 5) --> 1 + k ≡ 0 (mod 5) --> k ≡ 4 (mod 5)\r
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\n" ); document.write( "\n" ); document.write( "The first two equations imply k ≡ 1 (mod 6), so k can be 1, 7, 13, 19, 25, 31, ... The first value of k that is 4 modulo 5 is 19, so the smallest term in the sequence that satisfies is 17 + 7(19), or 150.\r
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