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Bunuel
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The first term in a certain sequence is 1, the 2nd term in the sequenc 04 Dec 2018, 01:35
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83% (02:21) correct 17% (02:19) wrong based on 128 sessions

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The first term in a certain sequence is 1, the 2nd term in the sequence is 2, and, for all integers n ≥ 3, the nth term in the sequence is the average (arithmetic mean) of the first n – 1 terms in the sequence. What is the value of the 6th term in the sequence?

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 2
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D
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The first term in a certain sequence is 1, the 2nd term in the sequenc 04 Dec 2018, 01:49
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Bunuel
The first term in a certain sequence is 1, the 2nd term in the sequence is 2, and, for all integers n ≥ 3, the nth term in the sequence is the average (arithmetic mean) of the first n – 1 terms in the sequence. What is the value of the 6th term in the sequence?

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 2
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3rd tem: 1+2/2= 1.5
4th term 1.5+1+2/3= 1.5
5th term (1.5+1.5+1.5+1+2)/4= 1.5

6th term: (1.5*3)+2+1 / 5= 3/2= IMO D
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The first term in a certain sequence is 1, the 2nd term in the sequenc 20 May 2020, 08:53
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Is there perhaps any bank of questions that are akin to this one?
Thank you!
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Bunuel
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The first term in a certain sequence is 1, the 2nd term in the sequenc 20 May 2020, 08:55
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malamacka
Is there perhaps any bank of questions that are akin to this one?
Thank you!
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Check our questions bank here: https://gmatclub.com/forum/search.php?view=search_tags

Hope it helps.
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The first term in a certain sequence is 1, the 2nd term in the sequenc 20 May 2020, 09:25
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Bunuel
malamacka
Is there perhaps any bank of questions that are akin to this one?
Thank you!

Check our questions bank here

Hope it helps.
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Helps very much.
Thank you!
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The first term in a certain sequence is 1, the 2nd term in the sequenc 25 May 2020, 11:43
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Bunuel
The first term in a certain sequence is 1, the 2nd term in the sequence is 2, and, for all integers n ≥ 3, the nth term in the sequence is the average (arithmetic mean) of the first n – 1 terms in the sequence. What is the value of the 6th term in the sequence?

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 2
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We see that

a(3) = (1 + 2)/2 = 3/2

a(4) = (1 + 2 + 3/2)/3 = (9/2)/3 = 3/2

a(5) = (1 + 2 + 3/2 + 3/2)/4 = 6/4 = 3/2

At this point, we can expect a(6) is also 3/2, but let’s calculate it anyway:

a(6) = (1 + 2 + 3/2 + 3/2 + 3/2)/5 = (15/2)/5 = 3/2

Answer: D
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