Question

Zhen and Justin made two different

number patterns that each started


at 0. Zhen wrote terms using the rule


"add 18." Justin wrote terms using the


rule "add 6." What is the relationship


between the two patterns?

Answer 1

Zhen pattern will be

Justin pattern will be

Since Zhen always add 18 and Justin always adds 6, and 6 is one third of 18, the n-th element of Zhen's pattern will always be three times the n-th element of Justin's pattern.

Answer 2

Zhen pattern will be

`0, 18, 36, 54, 72, 90,\ldots`

Justin pattern will be

`0, 6, 12, 18, 24, 30,\ldots`

Since Zhen always add 18 and Justin always adds 6, and 6 is one third of 18, the n-th element of Zhen's pattern will always be three times the n-th element of Justin's pattern.