For the following recursively defined function if f(x)=5 and f(x)=f(x-1)+6 find f(3)

Question

I just need it to be written out 

Answer 1

It is vital that you learn the concept of the recursion formula.  I do not think that you have defined this very well.

The normal way to specify this sequence of terms is to define f₁ = 5 [you could call it f(1) if you wish).

 

The next term is f₂ [or f(2)] and the RECURSION RULE IS f_n+1 = f_n + 6, for n being an integer from 1 and on up.

This one tells you that to get the next TERM, you take the prior term and add 6.

 

Although your may call this a function, it's not a function of all Real numbers a 'arguments'--the arguments or term # are the positive integers only. The graph of the sequence of f terms is not continuous anywhere.

 

NOW, the successive terms are 5, 11, 17, 23, etc. (starting with the first one).