What is the explicit formula for the following sequence { 1, 5, 9, 13,...}

Question

A.) an=4n-3

B.) an=n+4

C.) an=4n+5

D.) an=2n+1

Answer 1

A) an = 4n-3 is the correct answer.

 

In this particular type of problem n represents the index that you are at within the sequence.  So the n is 1 when at position the first number of the sequence and 2 at the second position in the sequence and so on.  Thus by simply plugging n to each corresponding an we can find which formula matches.  The answer is A is our winner here because as you can see when you plug in 1 into the formula you get (4*1) - 3 = 1.  Plug in 2 you get (4*2) - 3 = 5.  Plug in 3 you get (4*3) - 3 = 9.  It follows the pattern of the sequence shown and thus is the correct answer.