Asequence is defined by the rule f(n)=3f(n-1)+1. if f(1)=2 then f(3)=?

f(3) = 22

Step-by-step explanation:

To find f(3), we need to first find f(2) since we have been given f(1) to be equal to 2.

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

To find f(2), simply replace all the n in the function by 2

f(2)  = 3f(2-1) + 1

        =3f(1) + 1

but we were given f(1) to be equal to 2 from the question, so we will simply substitute f(1)=1 in the function

f(2) = 3f(1) + 1

      =3(2)  + 1

      =   6   + 1

      =7

so our f(2) = 7

We can now proceed to find f(3), to find f(3) simply replace all n by 3

f(3) = 3f(3-1) + 1

      =3f(2)  +  1

But we have gotten f(2) to be 7, so we simply substitute f(2) = 7 in the function.

f(3) = 3f(2) + 1

      =3(7)  + 1

      =21    + 1

      = 22

f(3) = 22

Therefore f(3) is 22