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Retired Moderator Joined: 07 Jun 2014
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Sn = 3n + 3 Sequence S is defined for each integer n such th [#permalink]
Expert's post 00:00

Question Stats: 79% (00:47) correct 20% (01:15) wrong based on 64 sessions
$$S_n = 3n + 3$$
Sequence S is defined for each integer n such that
0 < n < 10,000.

 Quantity A Quantity B The median of sequence S The mean of sequence S

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Sandy
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Re: Sn = 3n + 3 Sequence S is defined for each integer n such th [#permalink]
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Re: Sn = 3n + 3 Sequence S is defined for each integer n such th [#permalink]
Median of a sequence equals to mean of a sequence. C. GRE Instructor Joined: 10 Apr 2015
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Re: Sn = 3n + 3 Sequence S is defined for each integer n such th [#permalink]
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Expert's post
sandy wrote:
$$S_n = 3n + 3$$
Sequence S is defined for each integer n such that
0 < n < 10,000.

 Quantity A Quantity B The median of sequence S The mean of sequence S

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Let's examine a few terms in the sequence.

GIVEN: term_n = 3n + 3
So, term_1 = 3(1) + 3 = 6
term_2 = 3(2) + 3 = 9
term_3 = 3(3) + 3 = 12
term_4 = 3(4) + 3 = 15
term_5 = 3(5) + 3 = 18
etc

So, the sequence looks like this: 6, 9, 12, 15, 18, . . .

KEY CONCEPT: "In a set where the numbers are equally spaced, the mean will equal the median."
For example, in each of the following sets, the mean and median are equal:
{7, 9, 11, 13, 15}
{-1, 4, 9, 14}
{3, 4, 5, 6}

Since the numbers in the given set {6, 9, 12, 15, 18, . . .} are EQUALLY SPACED, the mean must equal the median

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  Intern Joined: 28 Aug 2018
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Re: Sn = 3n + 3 Sequence S is defined for each integer n such th [#permalink]
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C

Just remember one thing: numbers that are equally spaced always have the same mean and median.

Saves a ton of time during the test.
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Yuan Liu, Creator of Gregory. Dartmouth Grad.

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Re: Sn = 3n + 3 Sequence S is defined for each integer n such th [#permalink]
Expert's post
The mean and median are equally spaced, like Yuan says. if you know that then there's no need to calculate, but if you forget this rule, keep in mind..

just line up 1,2,3,4,5
the mean of this set is 3 and so is the median

plug each of these numbers into the series 3m+3, and we have

6,9,12,15,18 the median is still the middle of the set (12), and so is the mean (12)

this simpler example is a decent reminder. the answer is C Re: Sn = 3n + 3 Sequence S is defined for each integer n such th   [#permalink] 14 Jan 2019, 01:30
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