Answer:
111
Step-by-step explanation:
Arithmetic sequences are linear. That means no matter the pair of points use to calculate slope, or common difference, that number remains constant.
We are given points (1,-12) and (27,66) are on the line.
Calculating slope by subtracting points and then putting 2nd number over 1st.
(27,66)
(1, -12)
-----------subtracting
26 , 78
The slooe or the common difference is 78/26=3.
So now we want to know n such that (42,n) is on this same line.
Let's use the slope formula again with (42,n) and (1,-12).
(42,n)
( 1,-12)
----------subtracting
41 , n+12
The slope is (n+12)/41 but we have also calculated it to be 3 so these expressions are equal.
(n+12)/41=3
Multiply both sides by 41:
n+12=123
Subtract 12 on both sides.
n=111
