document.write( "Question 969778: Find the 1st term of this geometric sequence - 3 , 17 \n" ); document.write( "

Algebra.Com's Answer #592671 by KMST(5328) $\"\"$ $\"About$

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\n" ); document.write( "Is 3 the second term, and 17 the third term?
\n" ); document.write( "
\n" ); document.write( "If it is a geometric sequence, then each term is the one before times a fixed number, $\"r\"$ .
\n" ); document.write( "That number $\"r\"$ is called the common ratio, because it is the ratio between any two consecutive terms.
\n" ); document.write( "So, term number $\"n%2B1\"$ , $\"b%5Bn%2B1%5D\"$ ,
\n" ); document.write( "is related to the previous term,
\n" ); document.write( "term number $\"n\"$ = $\"b%5Bn%5D\"$ ,
\n" ); document.write( "by $\"b%5Bn%2B1%5D=b%5Bn%5D%2Ar\"$ <---> $\"r=b%5Bn%2B1%5D%2Fb%5Bn%5D\"$
\n" ); document.write( "for all natural number (counting number) values of $\"n\"$ .\r
\n" ); document.write( "\n" ); document.write( "IF 3 and 17 are consecutive terms,
\n" ); document.write( "then the common ratio between consecutive terms is
\n" ); document.write( " $\"r=17%2F3\"$ .
\n" ); document.write( "Each term is $\"17%2F3\"$ times the one before.
\n" ); document.write( "IF 3 and 17 are the 2nd and 3rd terms respectively,
\n" ); document.write( "then $\"b%5B2%5D=3\"$ , $\"b%5B3%5D=17\"$ , $\"r=17%2F3\"$ , and $\"b%5B1%5D\"$ is the first term that we want to find.
\n" ); document.write( "From $\"b%5Bn%2B1%5D=b%5Bn%5D%2Ar\"$ , for $\"n=1\"$ , we get
\n" ); document.write( " $\"b%5B1%2B1%5D=b%5B1%5D%2Ar\"$ ---> $\"b%5B2%5D=b%5B1%5D%2817%2F3%29\"$ ---> $\"3=b%5B1%5D%2817%2F3%29\"$
\n" ); document.write( "so ---> $\"b%5B1%5D%2817%2F3%29=3\"$ ---> $\"b%5B1%5D=3%2F%28%2817%2F3%29%29\"$ ---> $\"b%5B1%5D=3%283%2F17%29\"$ ---> $\"b%5B1%5D=9%2F17\"$ \n" ); document.write( "

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