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AM of preceding term

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by harsh.champ » Fri Feb 19, 2010 9:40 am
The first term in a sequence is 1 and the second term is 5. From the third term onwards 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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by outreach » Fri Feb 19, 2010 10:02 am
ans is 3
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by abhi332 » Fri Feb 19, 2010 12:10 pm
The first term in a sequence is 1 and the second term is 5. From the third term onwards 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
3rd term will be (1+5)/2 = 3
4th term will be (1+5+3)/3 = 3
5th term will be (1+5+3+3)/4 = 3

we can see that 3 is repeating,

IMO ans is B
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by harsh.champ » Fri Feb 19, 2010 12:13 pm
The OA [spoiler]is B - {3}.[/spoiler]

The soln. approach of abhi332 is perfect.
We just have to see that 3 is the repeating term.
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by ajith » Fri Feb 19, 2010 12:18 pm
harsh.champ wrote:The first term in a sequence is 1 and the second term is 5. From the third term onwards 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
x1 = 1
x2 = 5

x3 = 3
x4 = 3
x5 = 3

...
X25 = 3
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by shashank.ism » Sat Feb 20, 2010 5:54 am
harsh.champ wrote:The first term in a sequence is 1 and the second term is 5. From the third term onwards 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
T1 = 1
T2 = 5
so T3= (5+1)/2 = 3
T4 = (1+5+3)/3 =3
T5 = (1+5+3+3)/4 = 3

....
everytime only avg of all preceding terms is added so always 3 will be getting added . so 25 the tem of sequence will be 3 only
Ans B
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