As the number of CuO
2
layers,
n
, in each unit cell of a cuprate family increases, the maximum transition temperature (
T
c,max
) exhibits a universal bell-shaped curve with a peak at
n
= 3. The microscopic mechanism of this trend remains elusive. In this study, we used advanced electron microscopy to image the atomic structure of cuprates in the Bi
2
Sr
2
Ca
n
-1
Cu
n
O
2
n
+4+δ
family with 1 ≤
n
≤ 9; the evolution of the charge-transfer gap size (Δ) with
n
can be measured simultaneously. We determined that the
n
dependence of Δ follows an inverted bell-shaped curve with the minimum Δ value at
n
= 3. The correlation between Δ,
n
, and
T
c,max
may clarify the origin of superconductivity in cuprates.