GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jun 2018, 21:14

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

SVP
Status: Preparing for the GMAT
Joined: 02 Nov 2016
Posts: 1533
Location: Pakistan
GPA: 3.39
What is the one-thousandth term in sequence S ? [#permalink]

### Show Tags

03 Sep 2017, 23:42
00:00

Difficulty:

5% (low)

Question Stats:

91% (00:31) correct 9% (00:15) wrong based on 47 sessions

### HideShow timer Statistics

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.

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.

_________________

Official PS Practice Questions
Press +1 Kudos if this post is helpful

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1140
Location: India
GPA: 3.82
Re: What is the one-thousandth term in sequence S ? [#permalink]

### Show Tags

23 Sep 2017, 00:47
1
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.

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
Intern
Joined: 26 Sep 2017
Posts: 3
What is the one-thousandth term in sequence S ? [#permalink]

### Show Tags

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.

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?
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1140
Location: India
GPA: 3.82
Re: What is the one-thousandth term in sequence S ? [#permalink]

### Show Tags

26 Sep 2017, 21:12
1
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.

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.
Re: What is the one-thousandth term in sequence S ?   [#permalink] 26 Sep 2017, 21:12
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.