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+s_{1})+(1+s_{2})+(1+s_{3})= (1+F_{3})

s: spot rate

F: forward rate

Thank you