document.write( "Question 1161640: The first and the last term of an A.P are 21 and -47 respectively if the sum of the sequence is given is -234, calculate (I)the number of terms in the A.P (ii)the common difference (iii)the sum of the first is term \n" ); document.write( "

Algebra.Com's Answer #785245 by ikleyn(52797) $\"\"$ $\"About$

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document.write( "To find the number of terms, first calculate the average of the two endpoint terms\r\n" );
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document.write( "     = -13,\r\n" );
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document.write( "and then divide the given sum of the progression by this average\r\n" );
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document.write( "    n =  = 18.\r\n" );
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document.write( "So, the progression has 18 terms.\r\n" );
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document.write( "To find the common difference, first find the distance between the 1-st and the 18-th terms\r\n" );
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document.write( "    21 - (-47) = 21 + 47 = 68.\r\n" );
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document.write( "There are 17 equal gaps between the 1-st and 18-th terms; so each gap is \r\n" );
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document.write( "     = 4,\r\n" );
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document.write( "and each gap is equal to the common difference taken with the opposite sign.\r\n" );
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document.write( "ANSWER.  (i)  n = 18;  (ii) d = -4.\r\n" );
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\n" ); document.write( "\n" ); document.write( "So, the problem can be solved MENTALLY, without using equation, if you know the properties of arithmetic progressions.\r
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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( "    - Advanced problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Interior angles of a polygon and Arithmetic progression \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions solved MENTALLY \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( "\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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