diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index fd1bb3fe3e173..ba79fa9fe5120 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -656,7 +656,7 @@ cdef class BaseOffset:
         """
         dt = Timestamp(dt)
         if not self.is_on_offset(dt):
-            dt = dt - type(self)(1, normalize=self.normalize, **self.kwds)
+            dt = dt - type(self)(self.n, normalize=self.normalize, **self.kwds)
         return dt
 
     def rollforward(self, dt) -> datetime:
@@ -670,7 +670,7 @@ cdef class BaseOffset:
         """
         dt = Timestamp(dt)
         if not self.is_on_offset(dt):
-            dt = dt + type(self)(1, normalize=self.normalize, **self.kwds)
+            dt = dt + type(self)(self.n, normalize=self.normalize, **self.kwds)
         return dt
 
     def _get_offset_day(self, other: datetime) -> int:
diff --git a/pandas/tests/resample/test_datetime_index.py b/pandas/tests/resample/test_datetime_index.py
index dc2ddcc70828f..328c946d2eed3 100644
--- a/pandas/tests/resample/test_datetime_index.py
+++ b/pandas/tests/resample/test_datetime_index.py
@@ -2020,6 +2020,29 @@ def test_resample_empty_series_with_tz():
     tm.assert_series_equal(result, expected)
 
 
+def test_resample_quarters_non_unitary():
+    # https://github.com/pandas-dev/pandas/issues/29576
+
+    d = Series(
+        data=np.zeros(365), index=date_range("1950-01-01", "1950-12-31", freq="D")
+    )
+
+    actual = d.resample("2QS-MAR").mean()
+    expected_idx = DatetimeIndex(
+        np.array(
+            [
+                "1949-09-01",
+                "1950-03-01",
+                "1950-09-01",
+            ]
+        ).astype("datetime64[ns]"),
+        freq="2QS-MAR",
+    )
+    expected = Series(0.0, index=expected_idx)
+
+    tm.assert_series_equal(expected, actual)
+
+
 @pytest.mark.parametrize("freq", ["2M", "2m", "2Q", "2Q-SEP", "2q-sep", "1Y", "2Y-MAR"])
 def test_resample_M_Q_Y_raises(freq):
     msg = f"Invalid frequency: {freq}"