Answer
a) The output of the algorithm is 2 larger than the input.
$1\longrightarrow3$
$2\longrightarrow4$
$3\longrightarrow5$
$4\longrightarrow6$
b) $x+2$
c) The answer in part b and the conjecture in part a agree.
Work Step by Step
a) Apply the algorithm to several integers and examine the sequence to find a pattern.
1: $[(1\times3)+6]\div3=[3+6]\div3=9\div3=3$
2: $[(2\times3)+6]\div3=[6+6]\div3=12\div3=4$
3: $[(3\times3)+6]\div3=[9+6]\div3=15\div3=5$
4: $[(4\times3)+6]\div3=[12+6]\div3=18\div3=6$
b) Apply the algorithm to x and simplify. Use the distributive property to divide.
$[(x\times3)+6]\div3=[3x+6]\div3=3x\div3+6\div3=x+2$
c) Part a uses inductive reasoning because you are looking for a pattern in a sequence. Part b uses deductive reasoning because logic was used to reach the conclusion.
