Answer: Last option ("Each term in the second sequence is one-third the corresponding term in the first sequence.")
Explanation:
First, you need to understand what the rules are saying. I find it useful to write them as equations, but everyone's different. Especially for this situation, making a table should be really helpful.
Rule 1: add 6 starting from 0
Add 6 each time. The "add" part should tell you that it's the slope. The equation has a slope of 6. "Starting from 0" tells you that the y-intercept is 0. Using slope-intercept form (y=mx+b, where m is the slope and b is the y-intercept), you can write the equation as y=6x+0, or y=6x.
Rule 2: add 2 starting from 0
2 is the slope and 0 is the y-intercept. y=2x
You didn't <em>have</em> to do this part, but it makes the rules easier to understand. Now you can easily make a table to find the relationship between the rules. First, pick some values of x to use:
Rule 1:
x | 1 | 2 | 3
y | | |
Rule 2:
x | 1 | 2 | 3
y | | |
(They're supposed to be tables with only the x-values filled in.)
Using the equations, or only the rules, you can fill in the tables.
You can use more than 3 values of x, but I think this is enough.
x=1:
Rule 1: y=6x
=6(1)
=6
Rule 2: y=2x
=2(1)
=2
Do the same thing for y when x=2 and x=3. Then you can fill in the tables to get:
Rule 1:
x | 1 | 2 | 3
y | 6 | 12 | 18
Rule 2:
x | 1 | 2 | 3
y | 2 | 4 | 6
Since you've organized the values now, it'll be much simpler to find the relationship between the rules. Observe the y-values.
When x=1, rule 1 results in 6, and rule 2 results in 2. Now look at each option in the answers.
"Each term in the second sequence is three times the corresponding term in the first sequence."
In the first sequence, you have 6 when x=1. If the corresponding term in the second sequence has to be 3 times that, it would have to be 18. This one doesn't work.
"Each term in the first sequence is one-third the corresponding term in the second sequence."
This is saying the same thing as the previous option. It doesn't work.
"Each term in the first sequence is six times the corresponding term in the second sequence."
When x=1, y in the second sequence is 2. 6 times that is 12, but the value in the first sequence is only 6. This option is incorrect as well.
"Each term in the second sequence is one-third the corresponding term in the first sequence."
2/6=1/3, so this one does work. You could have arrivived at this conclusion earlier by just dividing, but I wanted to explain why the rest don't work.
Hope I could help!