The general term of an infinite sequence 9, 4, -1, -6,… is (u_{r} = ar + b). Find the values of a and b.
-
A.
a = 5, b = 14 -
B.
a = -5, b = 14 -
C.
a = 5, b = -14 -
D.
a = -5, b = -14
Correct Answer: Option B
Explanation
The terms of the sequence can be written as : (u_{r} = ar + b) in this case, being that they have a regular common difference for each of the r terms.
We can rewrite the sequence as (a + b, 2a + b, 3a + b,…) where a is the common difference of the sequence and b is a given constant gotten by solving
(a + b = 9) or (2a + b = 4) or any other one.
The common difference here is 4 – 9 = -1 – 4 = -5.
(-5 + b = 9 implies b = 9 + 5 = 14)
(therefore) The equation can be written as (u_{r} = -5r + 14).