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The first term in a sequence is 1 and the second term is 5. From the

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The first term in a sequence is 1 and the second term is 5. From the  [#permalink]

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New post 12 May 2016, 01:43
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The first term in a sequence is 1 and the second term is 5. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 25th term in the sequence?

A. 2.5
B. 3
C. 5
D. 25
E. 50

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Re: The first term in a sequence is 1 and the second term is 5. From the  [#permalink]

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New post 12 May 2016, 07:56
Bunuel wrote:
The first term in a sequence is 1 and the second term is 5. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 25th term in the sequence?

A. 2.5
B. 3
C. 5
D. 25
E. 50


The average of 2 first term will always be the next term begin from the 3th term

=> average of 1 and 5 is (1+5)/2 = 3
=> the next term will always be 3 => 25th term will be 3
=>answer is B (3)

Let's try another number:
let the first 2 term is 3 and 7 (because the last first 2 term was 1 and 5 , 1 and 5 are odd numbers , 5-1 = 4) = > 3 and 7 are odd numbers and 7-3 = 4

=> the average of 3 and 7 is (3+7)/2 = 5
=> the next term will always be 5
=> the 3th term will equal (3+7+5)/3 = 15/3 = 5
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The first term in a sequence is 1 and the second term is 5. From the  [#permalink]

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New post 12 May 2016, 07:58
Bunuel wrote:
The first term in a sequence is 1 and the second term is 5. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 25th term in the sequence?

A. 2.5
B. 3
C. 5
D. 25
E. 50


Hi
First term = 1...
second term = 5..
third term = \(\frac{(1+5)}{2} = 3\)...
Now we should realize that average of 3 terms is 3.. it will remain 3 for rest of the term..
fourth term =\(\frac{(1+5+3)}{3} = \frac{9}{3} = 3\)..
fifth term = \(\frac{(1+5+3+3)}{4} =\frac{12}{4} = 3\)

ans \(25th = 3\)
B
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Re: The first term in a sequence is 1 and the second term is 5. From the  [#permalink]

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New post 12 May 2016, 11:21
The answer is 'B'

1st Term= 1
2nd term= 5
3rd term= 6/2=3
4th term=1+5+3/3= 3

'3' is a repeating number after 3rd term
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Re: The first term in a sequence is 1 and the second term is 5. From the  [#permalink]

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Re: The first term in a sequence is 1 and the second term is 5. From the &nbs [#permalink] 01 Aug 2018, 09:40
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