document.write( "Question 1145696: The third term of an arithmetic sequence is -1 and the seventh term is -13; how would I find the explicit formula for this sequence, and what would a22 be? \n" ); document.write( "
Algebra.Com's Answer #766944 by ikleyn(52852)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Between the third term and the seventh term of an arithmetic progression, there are exactly 4 gaps in the number line \r\n" );
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document.write( "of equal sizes.\r\n" );
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document.write( "Hence, the common difference of the arithmetic progression (which is exactly the size of a single gap) is\r\n" );
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document.write( "    \"%28-13%29+-+%28-1%29%29%2F4\" = \"%28-12%29%2F4\" = -3.\r\n" );
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document.write( "Thus we just found that the common difference of the AP is -3.\r\n" );
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document.write( "Now it is easy to find its first term  \"a%5B1%5D\" = \"a%5B3%5D\" - 2*(-3) = -1 + 6 = 5.\r\n" );
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document.write( "Finally,  \"a%5B22%5D\" = \"a%5B1%5D\" + d*(22-1) = 5 + (-3)*21 = -58.    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( "    - Mathematical induction and arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Mathematical induction for sequences other than arithmetic or geometric\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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