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.