document.write( "Question 828533: Give AP -7,-3,1,....,state three consecutive terms in this AP which sum up to 75 \n" ); document.write( "

Algebra.Com's Answer #499367 by KMST(5328) $\"\"$ $\"About$

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In arithmetic progressions, given 3 term, the middle one is the average,
\n" ); document.write( "In other words, 3 consecutive terms add up to 3 times the middle term.
\n" ); document.write( "So, $\"75%2F3=25\"$ is the middle term.
\n" ); document.write( "The common difference is $\"1-%28-3%29=1%2B3=4\"$ ,
\n" ); document.write( "so the three terms are
\n" ); document.write( " $\"25-4=highlight%2821%29\"$ ,
\n" ); document.write( " $\"highlight%2825%29\"$ . and
\n" ); document.write( " $\"25%2B4=highlight%2829%29\"$ .
\n" ); document.write( "
\n" ); document.write( "How do I know that the average of 3 terms is the middle term?
\n" ); document.write( " $\"a%5Bn%5D=a%5Bn-1%5D%2Bd\"$ so $\"a%5Bn-1%5D=a%5Bn%5D-d\"$ ,
\n" ); document.write( "and $\"a%5Bn%2B1%5D=a%5Bn%5D%2Bd\"$ .
\n" ); document.write( "Adding them up you have
\n" ); document.write( " $\"a%5Bn-1%5D%2Ba%5Bn%5D%2Ba%5Bn%2B1%5D=%28a%5Bn%5D-d%29%2Ba%5Bn%5D%2B%28a%5Bn%5D%2Bd%29\"$
\n" ); document.write( " $\"a%5Bn-1%5D%2Ba%5Bn%5D%2Ba%5Bn%2B1%5D=a%5Bn%5D-d%2Ba%5Bn%5D%2Ba%5Bn%5D%2Bd\"$
\n" ); document.write( " $\"a%5Bn-1%5D%2Ba%5Bn%5D%2Ba%5Bn%2B1%5D=a%5Bn%5D%2Ba%5Bn%5D%2Ba%5Bn%5D\"$
\n" ); document.write( " $\"a%5Bn-1%5D%2Ba%5Bn%5D%2Ba%5Bn%2B1%5D=3%2Aa%5Bn%5D\"$ \n" ); document.write( "

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