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# What is the one-thousandth term in sequence S ?

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Status: Preparing for the GMAT
Joined: 02 Nov 2016
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What is the one-thousandth term in sequence S ? [#permalink]

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03 Sep 2017, 23:42
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Difficulty:

15% (low)

Question Stats:

96% (00:32) correct 4% (00:34) wrong based on 28 sessions

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What is the one-thousandth term in sequence S ?

(1) The fifth term in S is 47.
(2) Each term in S following the first term is generated by multiplying the preceding term by 4 and adding 1.

[Reveal] Spoiler:
The correct answer is (C). The rule for constructing the sequence is given
in (2). And the point of reference is given in (1). There is no need to try to find
the value of the thousandth term. You need only recognize that it is possible
to do so.
[Reveal] Spoiler: OA

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Kudos [?]: 1042 [0], given: 537

Senior Manager
Joined: 25 Feb 2013
Posts: 401

Kudos [?]: 170 [1], given: 31

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Re: What is the one-thousandth term in sequence S ? [#permalink]

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23 Sep 2017, 00:47
1
KUDOS
What is the one-thousandth term in sequence S ?

(1) The fifth term in S is 47.
(2) Each term in S following the first term is generated by multiplying the preceding term by 4 and adding 1.

[Reveal] Spoiler:
The correct answer is (C). The rule for constructing the sequence is given
in (2). And the point of reference is given in (1). There is no need to try to find
the value of the thousandth term. You need only recognize that it is possible
to do so.

To find $$T_{1000}$$

Statement 1: $$T_5=47$$. but no relation about other terms is given. Hence Insufficient

Statement 2: implies, $$T_n=4T_{n-1}+1$$. But value of no term is given. Hence Insufficient

Combining 1 & 2: We know the relation between terms and value of one term. Hence each term in the sequence can be calculated. Sufficient

Option C

Kudos [?]: 170 [1], given: 31

Intern
Joined: 26 Sep 2017
Posts: 3

Kudos [?]: 0 [0], given: 5

What is the one-thousandth term in sequence S ? [#permalink]

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26 Sep 2017, 17:56
niks18 wrote:
What is the one-thousandth term in sequence S ?

(1) The fifth term in S is 47.
(2) Each term in S following the first term is generated by multiplying the preceding term by 4 and adding 1.

[Reveal] Spoiler:
The correct answer is (C). The rule for constructing the sequence is given
in (2). And the point of reference is given in (1). There is no need to try to find
the value of the thousandth term. You need only recognize that it is possible
to do so.

To find $$T_{1000}$$

Statement 1: $$T_5=47$$. but no relation about other terms is given. Hence Insufficient

Statement 2: implies, $$T_n=4T_{n-1}+1$$. But value of no term is given. Hence Insufficient

Combining 1 & 2: We know the relation between terms and value of one term. Hence each term in the sequence can be calculated. Sufficient

Option C

Can you explain what I'm missing? Do we not need to know the first term? Each term in S following the first term is generated by multiplying the preceding term by 4 and adding 1.

How can we use the relation between terms if we don't know T4, T3, T2 and most importantly T1?

Kudos [?]: 0 [0], given: 5

Senior Manager
Joined: 25 Feb 2013
Posts: 401

Kudos [?]: 170 [1], given: 31

Location: India
GPA: 3.82
Re: What is the one-thousandth term in sequence S ? [#permalink]

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26 Sep 2017, 21:12
1
KUDOS
Manveetha wrote:
niks18 wrote:
What is the one-thousandth term in sequence S ?

(1) The fifth term in S is 47.
(2) Each term in S following the first term is generated by multiplying the preceding term by 4 and adding 1.

[Reveal] Spoiler:
The correct answer is (C). The rule for constructing the sequence is given
in (2). And the point of reference is given in (1). There is no need to try to find
the value of the thousandth term. You need only recognize that it is possible
to do so.

To find $$T_{1000}$$

Statement 1: $$T_5=47$$. but no relation about other terms is given. Hence Insufficient

Statement 2: implies, $$T_n=4T_{n-1}+1$$. But value of no term is given. Hence Insufficient

Combining 1 & 2: We know the relation between terms and value of one term. Hence each term in the sequence can be calculated. Sufficient

Option C

Can you explain what I'm missing? Do we not need to know the first term? Each term in S following the first term is generated by multiplying the preceding term by 4 and adding 1.

How can we use the relation between terms if we don't know T4, T3, T2 and most importantly T1?

Hi Manveetha

From Statement 2 we know that $$T_n=4T_{n-1}+1$$

so $$T_2=4*T_1+1$$. Similarly

$$T_3=4T_2+1 = 4(4*T_1+1)+1$$

$$T_4=4T_3+1= 4*[4(4*T_1+1)+1]+1$$

$$T_5=4T_4+1=4*[4*[4(4*T_1+1)+1]+1]+1$$.

Now you know the value of $$T_5$$, so substitute it in the last equation to get the value of $$T_1$$. Similarly you can $$T_{1000}$$ in terms of $$T_1$$ and hence the final answer.

As this is a DS question we do not need to actually calculate the value but only need to know that the value can be calculated and only a unique value is possible.

Kudos [?]: 170 [1], given: 31

Re: What is the one-thousandth term in sequence S ?   [#permalink] 26 Sep 2017, 21:12
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