SOLUTION: Use inductive reasoning to determine the next three numbers in the pattern: 1;1/3;1/9;1/27;... My Reasoning: I thought that 3 times 3 (from 1/3) is 9 and 3 times 9 (from the

Algebra ->  Sequences-and-series -> SOLUTION: Use inductive reasoning to determine the next three numbers in the pattern: 1;1/3;1/9;1/27;... My Reasoning: I thought that 3 times 3 (from 1/3) is 9 and 3 times 9 (from the      Log On


   

Question 190692: Use inductive reasoning to determine the next three numbers in the pattern:
1;1/3;1/9;1/27;...
My Reasoning:
I thought that 3 times 3 (from 1/3) is 9 and 3 times 9 (from the 1/9) is 27. So the next numbers would be 1/81;1/243;1/729 but I wasn't sure
Answer by user_dude2008(1862) About Me  (Show Source):
You can put this solution on YOUR website!
1 ---> 1/3 .... divide 1 by 3


1/3 ---> 1/9 .... divide 1/3 by 3 .... (1/3)/(3)=(1/3)(1/3)=1/9


1/9 ---> 1/27 .... divide 1/9 by 3 .... (1/9)/(3)=(1/9)(1/3)=1/27


etc...


Rule: divide term by 3 to get next term


1/27 ---> 1/81 .... divide 1/27 by 3 .... (1/27)/(3)=(1/27)(1/3)=1/81


1/81 ---> 1/243 .... divide 1/81 by 3 .... (1/81)/(3)=(1/81)(1/3)=1/243


1/243 ---> 1/729 .... divide 1/243 by 3 .... (1/243)/(3)=(1/243)(1/3)=1/729


Next 3 terms: 1/81, 1/243, 1/729