document.write( "Question 1100170: In the following two AP's how many terms are identical? 2,5,8,11....to 60 terms, 3,5,7...50 terms. \n" ); document.write( "

Algebra.Com's Answer #714786 by ikleyn(52792) $\"\"$ $\"About$

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\n" ); document.write( "In the following two AP's how many terms are identical? 2,5,8,11....to 60 terms, 3,5,7...50 terms.
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document.write( "Two progressions have the number 5 common as their second term, in each progression.\r\n" );
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document.write( "Further, the first  progression comes with the common difference 3, while \r\n" );
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document.write( "         the second progression comes with the common difference 2.\r\n" );
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document.write( "It means that, starting from their common second term of the value 5, they will have these CANDIDATES to be common terms:\r\n" );
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document.write( "    - every second term of the first progression. \r\n" );
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document.write( "    - every third term of the second progression.\r\n" );
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document.write( "We also should take care that the terms belong to their common range.\r\n" );
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document.write( "The last term of the 1-st AP is 2 + 59*3 = 179.\r\n" );
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document.write( "The last term of the 2-nd AP is 3 + 49*2 = 150.\r\n" );
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document.write( "So, the common range ends at 150.\r\n" );
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document.write( "Thus the amount of common members of the 1-st AP in this common range (starting and including 5) \r\n" );
document.write( "is  the integer part of the number , i.e. 25.\r\n" );
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document.write( "And now calculating the amount of common members of the 2-snd AP in this common range (starting and including 5) \r\n" );
document.write( "is the integer part of the number  gives the same 25  (ONLY FOR CHECKING).\r\n" );
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document.write( "Answer.  These two sequences have 25 numbers in common.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I think that the advise of the other tutor TO COUNT MANUALLY the common terms IS NOT THE SOLUTION and IS NOT THE METHOD OF SOLUTION.\r
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