document.write( "Question 1201664: Please help me with this problem\r
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\n" ); document.write( "\n" ); document.write( "Write a rule for the nth term of the arithmetic sequence where
\n" ); document.write( " 𝑎4 = 14 and 𝑎10 = 47 \n" ); document.write( "

Algebra.Com's Answer #836134 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Please help me with this problem\r
\n" ); document.write( "\n" ); document.write( "Write a rule for the nth term of the arithmetic sequence where
\n" ); document.write( "𝑎4 = 14 and 𝑎10 = 47
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document.write( "Write formulas for the 4th and 10th terms\r\n" );
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document.write( "    a4  = a1 + 3d = 14     (1)\r\n" );
document.write( "    a10 = a1 + 9d = 47     (2)\r\n" );
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document.write( "Subtract (1) from (2)\r\n" );
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document.write( "    9d - 3d = 47 - 14\r\n" );
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document.write( "       6d   =    33\r\n" );
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document.write( "        d   =    33/6 = 5.5.\r\n" );
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document.write( "Half of the problem is just solved.\r\n" );
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document.write( "Now from equation (1), \r\n" );
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document.write( "    a1 = 14 - 3*d = 14 -3*5.5 = 14 - 16.5 = -2.5.\r\n" );
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document.write( "Thus the first term of the AP is -2.5;  the common difference is d= 5.5.\r\n" );
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document.write( "Hence, the formula for the n-th term is\r\n" );
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document.write( "     = -2.5 + (n-1)*5.5 = -2.5 + 5.5n - 5.5 = -8 + 5.5n.    ANSWER\r\n" );
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