Answer: n = 13
Step-by-step explanation: While it may seem like there is a more complicated pattern behind this problem, there is actually a linear relationship.
We first notice that when X goes up by 2, Y goes up by 6. This could mean that if X goes up by 1, then Y goes up by 3. This is because in a linear relationship. X and Y are proportional. We also notice that when X goes up by 5 from 2 to 7, Y goes up by 15 from 4 to 19. If we divide 15 by 5, we get 3. This means that there is definitely a linear relationship.
If you have learned the concept of slope, you could treat the first two values of X and Y as points and find the slope between them. You could do the same for (4,10) and (7,19) or (2,4) and (7,19). In all these cases, we get a slope of 3 which indicates a linear relationship due to a constant rate of change.
Now that we have found the rule, we can solve for n. Since X goes up from 2 to 5, it goes up by 3. For each 1 that X goes up, Y goes up by 3. Therefore we multiply 3 by 3 to get 9. Y goes up by 9 from 4.
4 + 9 = 13 so Y is 13
Problems that require more advanced pattern recognition are not typical of math homework problems. To solve problems like this, use the formula for slope to find how much Y goes up for every increase in 1 X.
Hope this helps!