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The general term of an infinite sequence 9, 4, -1, -6,... is...

The general term of an infinite sequence 9, 4, -1, -6,... is ur=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 is B

The terms of the sequence can be written as : ur=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=9b=9+5=14

The equation can be written as u_{r} = -5r + 14.