document.write( "Question 1151680: Joe's annual income has been increasing each year by the same dollar amount. The first year his income was $19 comma 900, and the 4th year his income was $23 comma 800. In which year was his income $ 31 comma 600 question mark \n" ); document.write( "

Algebra.Com's Answer #773556 by ikleyn(52937) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            From the post by @rfer you may conclude that the answer is \"at the 9-th year\".\r
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\n" ); document.write( "\n" ); document.write( "            But do not hurry --- it would be wrong (!)\r
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\n" ); document.write( "\n" ); document.write( "            Read my solution below.\r
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document.write( "You start count that income from the first year:\r\n" );
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document.write( "    ,  , , . . . , .\r\n" );
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document.write( "The first term of this sequence is $19900.\r\n" );
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document.write( "It is arithmetic sequence, and its common difference is 1300, as @rfer correctly determined in his post.\r\n" );
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document.write( "Therefore, you can write \r\n" );
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document.write( "     = 1300 + (n-1)*1300.\r\n" );
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document.write( "You want to find \"n\" in a way that\r\n" );
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document.write( "    31600 = 1300 + (n-1)*1300.\r\n" );
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document.write( "It gives you\r\n" );
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document.write( "    n - 1 =  =  = 9.\r\n" );
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document.write( "    Hence,  n = 9+1 = 10.\r\n" );
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document.write( "ANSWER.  \"At which year ?\"  ----  at the 10-th year.\r\n" );
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\n" ); document.write( "\n" ); document.write( "So, the correct answer is \"at the 10-th year\"; or 9 years after the 1-st year.\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "From my post learn that not only calculations, but the entire conception of the solution and the answer itself
\n" ); document.write( "should be presented accurately -- if you want high scores.\r
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\n" ); document.write( "\n" ); document.write( "For introductory lessons on arithmetic progressions see \r
\n" ); document.write( "\n" ); document.write( "    - Arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Arithmetic progressions\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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