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S is a sequence s1, s2, s3,…,sn in which every term after the first is

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S is a sequence s1, s2, s3,…,sn in which every term after the first is  [#permalink]

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New post 08 May 2019, 01:05
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (02:47) correct 34% (03:00) wrong based on 53 sessions

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Re: S is a sequence s1, s2, s3,…,sn in which every term after the first is  [#permalink]

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New post 08 May 2019, 18:37
1
Bunuel wrote:
S is a sequence s1, s2, s3, …, sn in which every term after the first is one less than three times the previous term. If s5 – s3 = 28, which of the following is the first term in the sequence?

A. 2/3
B. 8/9
C. 1
D. 5/3
E. 2


s5-s3=28
or, 3s4-1-s3=28
or, 3(3s3-1)-1-s3=28
or, 8s3=32
or, s3=4
or, 3s2-1=4
or, 3(3s1-1)=5
or, 9s1=8
or, s1=8/9

Ans. (B)
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Re: S is a sequence s1, s2, s3,…,sn in which every term after the first is  [#permalink]

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New post 06 Jun 2020, 04:26
1
Bunuel wrote:
S is a sequence s1, s2, s3, …, sn in which every term after the first is one less than three times the previous term. If s5 – s3 = 28, which of the following is the first term in the sequence?

A. 2/3
B. 8/9
C. 1
D. 5/3
E. 2


Solution:


S1 = n

S2 = 3n - 1

S3 = 9n - 3 - 1 = 9n - 4

S4 = 27n - 12 - 1 = 27n - 13

S5 = 81n - 39 - 1 = 81n - 40

Since S5 - S3 = 28:

81n - 40 - (9n - 4) = 28

81n - 40 - 9n + 4 = 28

72n = 64

n = 64/72 = 8/9

Alternate Solution:

Instead of letting S1 = n, we can let S3 = n, so we have:

S4 = 3n - 1

S5 = 9n - 3 - 1 = 9n - 4

Since S5 - S3 = 28:

9n - 4 - n = 28

8n = 32

n = 4

Now, letting s = S2 (the second term), we have:

3s - 1 = 4

3s = 5

s = 5/3

Finally, letting f = S1 (the first term), we have:

3f - 1 = 5/3

3f = 8/3

f = 8/9

Answer: B
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Re: S is a sequence s1, s2, s3,…,sn in which every term after the first is   [#permalink] 06 Jun 2020, 04:26

S is a sequence s1, s2, s3,…,sn in which every term after the first is

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