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

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
The first term in a sequence is 1 and the second term is 5. From the  [#permalink]

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12 May 2016, 00:43
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15% (low)

Question Stats:

82% (01:25) correct 18% (01:43) wrong based on 78 sessions

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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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Joined: 07 May 2016
Posts: 26
Re: The first term in a sequence is 1 and the second term is 5. From the  [#permalink]

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12 May 2016, 06:56
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

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
Math Expert
Joined: 02 Aug 2009
Posts: 7106
The first term in a sequence is 1 and the second term is 5. From the  [#permalink]

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12 May 2016, 06:58
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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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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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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12 May 2016, 10:21

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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01 Aug 2018, 08:40
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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, 08:40
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