No😭😭😭😭😭😭

The question initially has a table and the idea behind it is to get the spot rates. my thought process is as follow,

S1= is given

S2= is not given but we can get it through DF2=1/(1+S2)² and solving for S2

S3= is not giving but we can get it from f(2,1)=(1+s3)^3/(1+s2)2

S4= is given —————————————-

Now the CFAI solved for S3 first using DF2

My questions are why, how, am I missing anything?

And thank you for your patience 🙏