## Thinking Mathematically (6th Edition)

a) $(4(1)+8)/2−4=2$ $(4(2)+8)/2−4=4$ $(4(3)+8)/2−4=6$ $(4(4)+8)/2−4=8$ $(4(5)+8)/2−4=10$ Conjecture: the result is the original number's double. b) Proof: for any $n$, the procedure is as follows: $n$, then $4n$, then $4n+8$, then $(4n+8)/2=2n+4$, then $(2n+4)−4=2n$, thus we always get back the original number's doible.