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: 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 \(u_{r} = -5r + 14\).
