Forward rate Vs Implied Forward rate?

CFA Level I Fixed Income
#1

hello everyone

what is the difference between the forward rate and implied forward rate?

why when i calculate the 1y2y implied forward rate the formula is

(1+x)(1+x)2 = (1+x)3

while for the same period forward rate

(1+s1)+(1+s2)+(1+s3)= (1+F3)

s: spot rate

F: forward rate

Thank you

#2

Your second formula makes no sense.

Where did you find it?