Simplifying a reverse Fold for a Query

A more direct solution with Fold using Range to reverse.

With

rfc[f_, g_, i_Integer?Positive] :=
 Fold[g[f[#2] /* #1] &, g[f[i]], Range[i - 1, 1, -1]]

Then

rfc[f, g, #] & /@ Range[4] // Column

g[f[1]]
g[f[1]/*g[f[2]]]
g[f[1]/*g[f[2]/*g[f[3]]]]
g[f[1]/*g[f[2]/*g[f[3]/*g[f[4]]]]]

Hope this helps.

fn[f_, g_, i_] :=
  g[ f[1] /* ## & @@ Array[g@*f, i - 1, 2] ]

Array[fn[f, g, #] &, 4] // Column

g[f[1]]
g[f[1] /* g[f[2]]]
g[f[1] /* g[f[2]] /* g[f[3]]]
g[f[1] /* g[f[2]] /* g[f[3]] /* g[f[4]]]

Oops, it seems this is a solution to a typo rather than what you actually need.

---

Responding to your comment for a solution to your variation:

fn[n_] := Fold[f[#2] /* g[#] &, f[n], Range[n - 1, 1, -1]]

Array[fn, 5] // Column

f[1]
f[1] /* g[f[2]]
f[1] /* g[f[2] /* g[f[3]]]
f[1] /* g[f[2] /* g[f[3] /* g[f[4]]]]
f[1] /* g[f[2] /* g[f[3] /* g[f[4] /* g[f[5]]]]]

Array[g@*fn, 5] // Column

g[f[1]]
g[f[1] /* g[f[2]]]
g[f[1] /* g[f[2] /* g[f[3]]]]
g[f[1] /* g[f[2] /* g[f[3] /* g[f[4]]]]]
g[f[1] /* g[f[2] /* g[f[3] /* g[f[4] /* g[f[5]]]]]]