AMC 10B/12B 2024 (Problem 4/4)

Balls numbered

1,2,3,\ldots

are deposited in 5 bins, labeled

A

B

C

D

, and

E

, using the following procedure. Ball 1 is deposited in bin

A

, and balls 2 and 3 are deposited in bin

B

. The next 3 balls are deposited in bin

C

, the next 4 in bin

D

, and so on, cycling back to bin

A

after balls are deposited in bin

E

. (For example, balls numbered

22,23,\ldots,28

are deposited in bin

B

at step 7 of this process.) In which bin is ball 2024 deposited?

\text{(A)}\;\text{A}

\text{(B)}\;\text{B}

\text{(C)}\;\text{C}

\text{(D)}\;\text{D}

\text{(E)}\;\text{E}