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# Let H be a sequence, h1 , h2 , h3…hn , such that each term after the

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
Let H be a sequence, h1 , h2 , h3…hn , such that each term after the  [#permalink]

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20 Feb 2019, 00:32
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Difficulty:

35% (medium)

Question Stats:

70% (02:10) correct 30% (02:45) wrong based on 30 sessions

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Let H be a sequence, h1, h2, h3…hn, such that each term after the first is two less than one-third of the previous term. If the fourth term in the sequence is 0, which of the following is the sum of the first and fifth terms of the sequence?

A.−2
B. 76/3
C. 26
D. 76
E. 78

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Re: Let H be a sequence, h1 , h2 , h3…hn , such that each term after the  [#permalink]

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20 Feb 2019, 03:04
Bunuel wrote:
Let H be a sequence, h1, h2, h3…hn, such that each term after the first is two less than one-third of the previous term. If the fourth term in the sequence is 0, which of the following is the sum of the first and fifth terms of the sequence?

A.−2
B. 76/3
C. 26
D. 76
E. 78

Hence from the question stem:

Xn= X(n-1)/3 - 2
=> X(n-1) = (2 + Xn)*3

So if X4=0
then X5= (0/3)-2 = -2

also
=> X3 = (2 + 0)*3 = 6
=> X2 = (6 + 2)*3 = 24
=> X1 = (2 + 24)*3 = 78

X1 + X5 = 78 + (-2) = 76

Hence D is the correct answer.
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Re: Let H be a sequence, h1 , h2 , h3…hn , such that each term after the  [#permalink]

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21 Feb 2019, 07:52
Bunuel wrote:
Let H be a sequence, h1, h2, h3…hn, such that each term after the first is two less than one-third of the previous term. If the fourth term in the sequence is 0, which of the following is the sum of the first and fifth terms of the sequence?

A.−2
B. 76/3
C. 26
D. 76
E. 78

h1=x
h2=(x/3)-2
h3=h2/3-2
h4=0
h4=h3/3-2
h3= 6
h2=24
h1=78
and h5=-2
so h1+h5 = 76
IMO D
Re: Let H be a sequence, h1 , h2 , h3…hn , such that each term after the   [#permalink] 21 Feb 2019, 07:52
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