f(1)=2, The sequence 2,5,8,11,14... is what kind of a sequence

Question

f(1)=2, The sequence 2,5,8,11,14... is what kind of a sequence

Answer 1

The sequence has a starting value --  f(1)=2.

 

Then, there are more values, like f(2)=5 and so on.

 

Now, to go from 2 to 5 allows many possibilities for a "rule," so more values are given.  First, look for a "common difference" between the values.  Each value given is 3 more than the current value.  That rule looks like this:

 

       f(n) = f(n-1) + 3    with f(1)=2

 

When there is a common difference (the constant value d), we have a rule for an Arithmetic Sequence.

 

       f(n) = f(n-1) + d    with f(1)=2 and d=3