a, b, c, d, e

An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant. If the list of numbers shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?

I. \(a − 3, b − 3, c − 3, d − 3, e − 3\)
II. \(a^3, b^3, c^3, d^3, e^3\)
III. \(4a, 4b, 4c, 4d, 4e
\)

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III



Kudos for the right answer and explanation
Question part of the project GRE Quant/Math Extreme Challenge Daily (2021) Edition
GRE - Math Book