document.write( "Question 1063744: The sum of the first 5 terms of an AP is 30 and the fourth term is 44 find the common difference and the sum of the first 10 terms \n" ); document.write( "

Algebra.Com's Answer #678872 by ikleyn(52797) $\"\"$ $\"About$

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\n" ); document.write( "The sum of the first 5 terms of an AP is 30 and the fourth term is 44 find the common difference and the sum of the first 10 terms
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document.write( "Let \"x\" be the THIRD term and \"d\" be the common difference. \r\n" );
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document.write( "Then the first 5 terms of the progression are\r\n" );
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document.write( "x - 2d, x-d, x, x+d, x + 2d,\r\n" );
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document.write( "and their sum is 5x.\r\n" );
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document.write( "Since the sum of the first 5 terms of the AP is 30, you have this equation\r\n" );
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document.write( "5x = 30,  which implies x = 6.\r\n" );
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document.write( "So, you just found the third term. It is 6.\r\n" );
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document.write( "Now, since the 4-th term is 44, the common difference is 44-6 = 38.\r\n" );
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document.write( "Then the second term is 6-38 = -32 and the first term is -32 - 38 = -70.\r\n" );
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document.write( "So, you know all and everything about the progression: The first term is -70 and the common difference is 38.\r\n" );
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document.write( "Can you complete the assignment on your own from this point ?\r\n" );
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\n" ); document.write( "\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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