We consider two variants of transfinite induction, one with monotonicity assumption on the predicate and one with the induction hypothesis only for cofinally many below. The latter can be seen as a transfinite analogue of the successor induction, while the usual transfinite induction is that of cumulative induction. We calculate the supremum of ordinals along which these schemata for $$\varDelta _0$$ formulae are provable in $$\mathbf {I}\varvec{\Sigma }_n$$. It is shown to be larger than the proof-theoretic ordinal $$|\mathbf {I}\varvec{\Sigma }_n|$$ by power of base 2. We also show a similar result for the structural transfinite induction, defined with fundamental sequences.