Carcass wrote:
\(v, w, x, y, z\)
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. \(2v, 2w, 2x, 2y, 2z\)
II. \(v + 2, w + 2, x + 2, y + 2, z + 2\)
III. \(\sqrt{v},\sqrt{w},\sqrt{x},\sqrt{y},\sqrt{z}\)
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Let the sequence be 1, 2, 3, 4, 5
I. 2, 4, 6, 8, 10
A.P with common difference of 2
II. 3, 4, 5, 6, 7
Again an A.P with common difference
III. 1, 1.41, 1.73, 2, 2.23
Not an A.P
Hence, option D