document.write( "Question 1091923: The third term of an arithmetic sequence is 8 and the sixth term is 2. Find the 30th term \n" ); document.write( "
Algebra.Com's Answer #706416 by ikleyn(52794)\"\" \"About 
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\n" ); document.write( "The third term of an arithmetic sequence is 8 and the sixth term is 2. Find the 30th term
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document.write( "\"a%5B3%5D\" = 8 = \"a%5B1%5D+%2B+2d\".   (1)   (\"a%5B1%5D\" is the first term of the AP)\r\n" );
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document.write( "\"a%5B6%5D\" = 2 = \"a%5B1%5D+%2B+5d\".   (2)   (d is the common difference of the AP)\r\n" );
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document.write( "Subtract eqn(1) from eqn(2). You will get\r\n" );
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document.write( "5d - 2d = 2 - 8,   or   3d = -6.   Hence, d = \"-6%2F3\" = -2.\r\n" );
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document.write( "Now \"a%5B30%5D\" = \"a%5B1%5D+%2B+29d\" = \"%28a%5B1%5D%2B2d%29\" + \"27d\" = \"a%5B3%5D+%2B+27d\" = 8 + 27*(-2) = 8 - 54 = -46.\r\n" );
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document.write( "Answer.  \"a%5B30%5D\" = -46.\r\n" );
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document.write( "To confirm my solution, I prepared this Table in Excel on my computer.\r\n" );
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document.write( "n    \"a%5Bn%5D\"\r\n" );
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document.write( "1	         I do not need the terms \"a%5B1%5D\" and \"a%5B2%5D\",\r\n" );
document.write( "2	         so I left these cells empty.\r\n" );
document.write( "3	8\r\n" );
document.write( "4	6\r\n" );
document.write( "5	4\r\n" );
document.write( "6	2\r\n" );
document.write( "7	0\r\n" );
document.write( "8	-2\r\n" );
document.write( "9	-4\r\n" );
document.write( "10	-6\r\n" );
document.write( "11	-8\r\n" );
document.write( "12	-10\r\n" );
document.write( "13	-12\r\n" );
document.write( "14	-14\r\n" );
document.write( "15	-16\r\n" );
document.write( "16	-18\r\n" );
document.write( "17	-20\r\n" );
document.write( "18	-22\r\n" );
document.write( "19	-24\r\n" );
document.write( "20	-26\r\n" );
document.write( "21	-28\r\n" );
document.write( "22	-30\r\n" );
document.write( "23	-32\r\n" );
document.write( "24	-34\r\n" );
document.write( "25	-36\r\n" );
document.write( "26	-38\r\n" );
document.write( "27	-40\r\n" );
document.write( "28	-42\r\n" );
document.write( "29	-44\r\n" );
document.write( "30	-46\r\n" );
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\n" ); document.write( "There is a bunch of lessons on arithmetic progressions in this site:\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( "    - Mathematical induction 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
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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\r
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\n" ); document.write( "\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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