document.write( "Question 933070: first term a, common difference d \r
\n" ); document.write( "\n" ); document.write( "the sum of the first 200 terms is 4 times the sum of the first 100 terms\r
\n" ); document.write( "\n" ); document.write( "-find d in terms of a\r
\n" ); document.write( "\n" ); document.write( "-find the 100th term in terms of a \n" ); document.write( "

Algebra.Com's Answer #566594 by KMST(5328) $\"\"$ $\"About$

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The sum of the first $\"n\"$ terms is
\n" ); document.write( " $\"%282a%2B%28n-1%29%2Ad%29%28n%2F2%29\"$ , so
\n" ); document.write( "the sum of the first $\"200\"$ terms is
\n" ); document.write( " $\"%282a%2B%28200-1%29d%29%28200%2F2%29=%282a%2B199d%29%28100%29=200a%2B19900d\"$ , and
\n" ); document.write( "the sum of the first $\"n\"$ terms is
\n" ); document.write( " $\"%282a%2B%28100-1%29d%29%28100%2F2%29=%282a%2B99d%29%2850%29=100a%2B4950d\"$ .
\n" ); document.write( "Since the sum of the first 200 terms is 4 times the sum of the first 100 terms,
\n" ); document.write( " $\"200a%2B19900d=4%28100a%2B4950d%29\"$
\n" ); document.write( " $\"200a%2B19900d=400a%2B19800d\"$
\n" ); document.write( " $\"100d=200a\"$
\n" ); document.write( " $\"d=200a%2F100\"$
\n" ); document.write( " $\"highlight%28d=2a%29\"$
\n" ); document.write( "The $\"n%5Eth\"$ therm is $\"a%2B%28n-1%29%2Ad\"$ , so the $\"100%5Eth\"$ term is
\n" ); document.write( " $\"a%2B%28n-1%29%2A%282a%29=a%281%2B%28n-1%29%2A2%29=a%281%2B2n-2%29=highlight%28a%282n-1%29%29\"$ . \n" ); document.write( "

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