document.write( "Question 1070095: The 12th 85th and last terms of an arithmetic progression are 38 257 and 395 respectively. Find the number of term.
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Algebra.Com's Answer #685246 by Fombitz(32388) $\"\"$ $\"About$

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$\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"$
\n" ); document.write( " $\"a%5B12%5D=a%5B1%5D%2B%2812-1%29d=38\"$
\n" ); document.write( " $\"a%5B1%5D%2B11d=38\"$
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\n" ); document.write( " $\"a%5B1%5D%2B84d=257\"$
\n" ); document.write( "Subtracting the first equation from this equation,
\n" ); document.write( " $\"a%5B1%5D%2B84d-a%5B1%5D-11d=257-38\"$
\n" ); document.write( " $\"73d=219\"$
\n" ); document.write( " $\"d=3\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"a%5B1%5D%2B11%283%29=38\"$
\n" ); document.write( " $\"a%5B1%5D%2B33=38\"$
\n" ); document.write( " $\"a%5B1%5D=5\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"a%5B1%5D%2B%28k-1%29d=395\"$
\n" ); document.write( "Find k.
\n" ); document.write( " $\"5%2B%28k-1%293=395\"$
\n" ); document.write( " $\"%28k-1%293=390\"$
\n" ); document.write( " $\"k-1=130\"$
\n" ); document.write( " $\"k=131\"$
\n" ); document.write( "131 terms \n" ); document.write( "

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