Question

What are the next three terms in the sequence 4, -1, -6, -11, ...?

Answer 1

Answer:

In summary, "the next three terms" are {-16, -21, -26}

Step-by-step 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}