Answer:
In summary, "the next three terms" are {-16, -21, -26}
Explanation:
Note that the common difference separating the terms of 4, -1, -6, -11, ... is -5. Each new term is found by combining the previous term with -5.
Thus, the applicable formula is a(n) = 4-5(n-1).
We should test this. Take the term -6 and determine whether or not this formula correctly predicts the next term: -11:
a(4) = 4-5(4-1) = 4 - 5(3) = 4 - 15 = -11 (yes).
We have the first four terms and need the 5th, 6th and 7th terms.
The fifth term, a(5), is 4-5(5-1) = 4-20 = -16
The sixth term is a(6) = 4-5(6-1) = -21
The seventh term is a(7) = 4 -5(6) = -26
In summary, "the next three terms" are {-16, -21, -26}