Check if the mapping is a linear/arithmetic sequence by finding the difference between each consecutive value of
y. A linear sequence has the common difference between consecutive numbers the same
If it is linear, use the equation of linear formula to find the rule of the mapping
y2−y1=9−5=4y3−y2=13−9=4y4−y3=17−13=4y5−y4=21−17=4As you can see, the rule of the mapping is a linear since the difference is the same, hence use the linear sequence formula to find the rule
Un=U1+(n−1)d Where
Un is the value at the
nth position, in the rule of mapping, the
y value
U1 is the first term, in the mapping above, 5
d is the common difference between each consecutive terms
n is the position, in the case of the above mapping,
x y=5+(x−1)4y=5+(x−1)×4y=5+x×4−1×4y=5+4x−4y=4x+5−4y=4x+1We can test with when
x=3y=4x+1y=4×3+1y=12+1=13 You can try the values of x to see if you will get the corresponding y value to prove the rule is correct
| x | y=4x+1 | y |
|---|
| 1 | y=4×1+1=4+1=5 | 5 |
| 2 | y=4×2+1=8+1=9 | 9 |
| 3 | y=4×3+1=12+1=13 | 13 |
| 4 | y=4×4+1=16+1=17 | 17 |
| 5 | y=4×5+1=20+1=21 | 21 |