document.write( "Question 929247: As I was going to St. Ives, I met a man with 7 wives, every wife had 7 sacks, and every sack had 7 cats. Every cat had 7 kits. Kits, cats, sacks, wives, how many were going to St. Ives? A.) use a geometric series to model as a sum the number of items (kits,cats,sacks,wives,man) that the narrator met. B.) evaluate this geometric series in 2 ways: directly by adding the terms, and also by using the summation formula that was developed. \n" ); document.write( "

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A)
\n" ); document.write( "The first term is $\"t%5B1%5D=1\"$ for 1 man.
\n" ); document.write( "The second term is $\"t%5B2%5D=1%2A7=7\"$ for the 7 wives per man for that 1 man.
\n" ); document.write( "The third term is $\"t%5B3%5D=t%5B2%5D%2A7=7%2A7=49\"$ for the 7 sacks per wife times 7 wives.
\n" ); document.write( "We see that we have a geometric sequence, with common ratio $\"r=7\"$ , and each term will be according to $\"t%5Bn%5D=t%5B1%5D%2Ar%5E%28n-1%29=1%2A7%5E%28n-1%29=7%5E%28n-1%29\"$
\n" ); document.write( "The fourth term is $\"t%5B4%5D=7%5E3=343\"$ representing the total number of cats.
\n" ); document.write( "The fifth term is $\"t%5B5%5D=7%5E4=2401\"$ representing the total number of cats.\r
\n" ); document.write( "\n" ); document.write( "B) The sum the number of items (kits,cats,sacks,wives,man) that the narrator met is
\n" ); document.write( " $\"1%2B7%2B49%2B343%2B2401=2801\"$ (directly by adding the terms).
\n" ); document.write( "Since the sum of a geometric series can be calculates as
\n" ); document.write( " $\"S%5Bn%5D=t%5B1%5D%2A%28%28r%5En-1%29%2F%28r-1%29%29\"$ ,
\n" ); document.write( "in this case the sum is $\"S%5B5%5D=1%2A%28%287%5E5-1%29%2F%287-1%29%29=%2816807-1%29%2F6=16806%2F6=2801\"$ \n" ); document.write( "

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