document.write( "Question 1159788: The fifth term of an arithmetic progression is three times the second term,and the third term is 10.find the 20th term? \n" ); document.write( "

Algebra.Com's Answer #782854 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "Let \"a\" be the first term of the AP, and let \"d\" be its common difference.\r\n" );
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document.write( "Then from the condition you have these two equations\r\n" );
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document.write( "    3*(a+d) = a + 4d      (1)    (which means   =  )\r\n" );
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document.write( "    a + 2d  = 10          (2)    (which means   = 10 )\r\n" );
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document.write( "From equation (1)\r\n" );
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document.write( "    3a + 3d = a + 4d\r\n" );
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document.write( "     2a     = d           (3)\r\n" );
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document.write( "From equation (2)\r\n" );
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document.write( "     2a + 4d = 20,\r\n" );
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document.write( "and substituting (replacing) here 2a = d  from (3), you get\r\n" );
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document.write( "    d  + 4d = 20,\r\n" );
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document.write( "    5d      = 20,\r\n" );
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document.write( "     d      = 20/5 = 4.\r\n" );
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document.write( "Now from equation (2)\r\n" );
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document.write( "    a = 10-3d = 10-2*4 = 2.\r\n" );
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document.write( "So, the progression has the first term  a= 2  and  the common difference  d= 4.\r\n" );
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document.write( "In particular, the 20-th term is\r\n" );
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document.write( "     = a + 19*d = 2 + 19*4 = 78.      ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "On arithmetic progressions, see the lessons\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( "    - Chocolate bars and arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - One characteristic property of arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Calculating partial sums of arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Finding number of terms of an arithmetic progression \r
\n" ); document.write( "\n" ); document.write( "    - Advanced problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions solved MENTALLY \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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