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v, w, x, y, z A geometric sequence is a sequence in which each term after the fi rst is equal to the product of the preceding term and a constant. If the list of numbers shown above is an geometric sequence, which of the following must also be a geometric 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) I and III

i) let's say orig sequence v, w, x, y, z = a, ba, b*ba, b*b*ba.. then 2v, 2w, 2x, 2y, 2z will be, 2a, 2ba, 2b*ba, 2*b*b*ba... every number is still a multiplication of the previous term by the constant - b

iii) again lets say v, w, x, y, z = a, ba, b*ba, b*b*ba.. then \sqrt{v}, \sqrt{w}, \sqrt{x}, \sqrt{y}, \sqrt{z} = \(\sqrt{a}, \sqrt{ba}, \sqrt{b*b*a}, \sqrt{b*b*ba}\)...

The first term in the sequence is now \(\sqrt{a}\), and every term in the new sequence is still equal to the previous term multiplied by a constant - \(\sqrt{b}\)

lets say series is 2,4,8,16,32 where common multiple is 2 let us multiply each term by 3, new series becomes 6,12,24,48,96 which is again a GP whose common multiple is 2

same case applies for square root

while adding 2 to each term will not generate any GP

gmatclubot

Re: geometric sequence
[#permalink]
19 Dec 2011, 03:10