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

A.) - 16, - 21, - 26

B.) - 14, - 21, - 26

C.) - 14, - 17, - 20

D.) - 18, - 25, - 32

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}