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what is the sum of the first four terms of sequence S?

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what is the sum of the first four terms of sequence S?  [#permalink]

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New post 01 Jul 2016, 04:57
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A
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Difficulty:

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Question Stats:

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What is the sum of the first four terms of sequence S?

(1) After the first two terms of S,the value of each term of S is equal to the average (arithmetic mean) of the last two preceding terms.

(2) The average (arithmetic mean) of the first three terms of S is 10.

OG Q 2017 New Question(Book Question: 219)

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Re: what is the sum of the first four terms of sequence S?  [#permalink]

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New post 01 Jul 2016, 06:33
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AbdurRakib wrote:
What is the sum of the first four terms of sequence S?

(1) After the first two terms of S,the value of each term of S is equal to the average (arithmetic mean) of the last two preceding terms.

(2) The average (arithmetic mean) of the first three terms of S is 10.

OG Q 2017 New Question(Book Question: 219)


E

Assume 1st term a nd 2nd term b.

From 1st statement, 3rd term (c) = (a+b)/2

4th term = (b +c)/2

From 2nd statement, (a+b+c)/3 =10
a+b+ (a+b)/2 =30

a+b = 20
Therefore, c=10

4th term = (b+c)/2

( we find out the sum of a and b but we can't say anything about individual values. Since, a can be 1,2.....so on and correspondingly b can be 19,18....so on)

So the answer is E






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Re: what is the sum of the first four terms of sequence S?  [#permalink]

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New post 05 Aug 2018, 16:54
AbdurRakib wrote:
What is the sum of the first four terms of sequence S?

(1) After the first two terms of S,the value of each term of S is equal to the average (arithmetic mean) of the last two preceding terms.

(2) The average (arithmetic mean) of the first three terms of S is 10.

OG Q 2017 New Question(Book Question: 219)


(1) We could make S anything.

Not Sufficient.


(2) Plug in numbers.

9, 10, 11, 100. Satisfies statement and sum is 130
9, 10, 11, 12. Satisfies statement and sum is 42.

Not Sufficient.


(1) + (2) Plug in numbers.

9, 11, 10, 10.5. Satisfies both statments and sum is 40.5

5, 15, 10, 12.5. Satisfies both statements and sum is 42.5

Not Sufficient.

Answer: E
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Re: what is the sum of the first four terms of sequence S?  [#permalink]

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New post 06 Aug 2019, 05:55
WHAT IS THE BEST APPROACH TO SOLVE SUCH PROBLEM ?
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Re: what is the sum of the first four terms of sequence S?  [#permalink]

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New post 17 Aug 2019, 20:51
09173140521 wrote:
WHAT IS THE BEST APPROACH TO SOLVE SUCH PROBLEM ?


According to statement 1 = x + y + (x+y)/2 + [(x+y)/2 + y]/2 = S

No info about Sum, NS.

St 2- x+y+z = 30.

NS.

On combining,

x + y + (x+y)/2 = 30 => x+y = 20.

We can find the 3rd term with this info but since we have no idea what type of sequence it is w.r.t first three terms, we cannot determine x & y.

FYI, 3rd term will be (x+y)/2 = 10. (replacing x+y with 20). But, can you find x & y ? (x+y =20 ...x & y could be multiple values)
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Re: what is the sum of the first four terms of sequence S?   [#permalink] 17 Aug 2019, 20:51
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