It is currently 15 Dec 2017, 04:29

Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1 | UCLA R1


Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn

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

Hide Tags

4 KUDOS received
Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 531

Kudos [?]: 4319 [4], given: 217

Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

Show Tags

New post 20 Mar 2012, 08:00
4
This post received
KUDOS
29
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:18) correct 20% (01:06) wrong based on 576 sessions

HideShow timer Statistics

In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = -4?

A. -1
B. 7
C. 10
D. 14
E. 20
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Kudos [?]: 4319 [4], given: 217

7 KUDOS received
Intern
Intern
User avatar
Joined: 04 Feb 2012
Posts: 6

Kudos [?]: 16 [7], given: 0

Location: Greece
Concentration: Entrepreneurship, General Management
GMAT Date: 03-07-2012
WE: General Management (Real Estate)
Re: Arithmetic Sequence [#permalink]

Show Tags

New post 20 Mar 2012, 08:42
7
This post received
KUDOS
4
This post was
BOOKMARKED
well.....t2 =t1-3 =23-3=20

t3=t2-3=20-3=17

So every time we n increases tn decreases by 3.

Since t1=23 we have 23-3=20-3=17-3=14-3=11-3=8-3=5-3=2-3=-1-3=-4!VOILA

So n=10 ten times substructing 3 from 23 to reach -4.

clear :?: :-D

Kudos [?]: 16 [7], given: 0

Expert Post
11 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42620

Kudos [?]: 135707 [11], given: 12706

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

Show Tags

New post 20 Mar 2012, 12:44
11
This post received
KUDOS
Expert's post
17
This post was
BOOKMARKED
enigma123 wrote:
In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = -4?

A. -1
B. 7
C. 10
D. 14
E. 20

I struggled badly on this question? Can you please help?


\(t_n=t_{n-1}-3\) means that each term is 3 less than the previous term. Now, the difference between \(t_1=23\) and \(t_n=-4\) is \(23-(-4)=27\), so we moved \(\frac{27}{3}=9\) terms from \(t_1\), so from \(t_1\) to \(t_{10}\).

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135707 [11], given: 12706

13 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 380

Kudos [?]: 412 [13], given: 73

Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
GMAT ToolKit User
Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

Show Tags

New post 12 Apr 2012, 09:24
13
This post received
KUDOS
1
This post was
BOOKMARKED
tn= tn-1 - 3 means that d=-3

tn=t1 +d(n-1)
-4=23-3(n-1)
-30=-3n
n=10
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Kudos [?]: 412 [13], given: 73

4 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1849

Kudos [?]: 2790 [4], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

Show Tags

New post 22 Apr 2014, 01:15
4
This post received
KUDOS
2
This post was
BOOKMARKED
23... 20.... 17... 14... 11.... 8... 5... 2.... -1.... -4

-4 is the 10th term

Answer = 10
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2790 [4], given: 193

2 KUDOS received
Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 437

Kudos [?]: 144 [2], given: 169

Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

Show Tags

New post 03 Feb 2015, 00:44
2
This post received
KUDOS
I also did the same as Paresh, but like this:

We know that t1 = 23
So, using the given formula we have:
t1=(t1-1) -3 =23
t0 - 3 = 23
t0= 26

The sam way we find that t2= 20

It seems that the sequence goes like this:
t0 = 26
t1 = 23
t2 = 20
t3 = 17
t4 = 14
t5 = 11
t6 = 8
t7 = 5
t8 = 2
t9 = -1
t10 = -4

So, our ANS is C.

However, I did do it wrong because, by the way I saw it writen, I though that the whole formula equaled to 23 (t1, t2, t3, ..., tn, t1=23). I didn't see any relationship as to why this is 23 (it is an addition, is it a multiplication?). So, then I thought that what was meant is that this sequence is doing a circle, going from t1 to t1 again, and there are 23 numbers in the sequence. So, I though we needed to find tn.

Hopefully the gmat would show in a more clear way that t1=23 and not the whole sequence..

Kudos [?]: 144 [2], given: 169

1 KUDOS received
Intern
Intern
avatar
B
Joined: 22 Jul 2016
Posts: 27

Kudos [?]: 8 [1], given: 33

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

Show Tags

New post 08 Jan 2017, 23:59
1
This post received
KUDOS
t1=23
t2=t1-3=20
t3=t2-3=17 and so on...
Here is when we need to consider the formula for AP as we know the common difference is -3

tn=t1 + d(n-1)

given, tn=-4
-4=23 + (-3) (n-10) >> n=10

Ans : C

Kudos [?]: 8 [1], given: 33

Intern
Intern
avatar
B
Joined: 07 Sep 2016
Posts: 6

Kudos [?]: [0], given: 1

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

Show Tags

New post 09 Jan 2017, 02:17
enigma123 wrote:
In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = -4?

A. -1
B. 7
C. 10
D. 14
E. 20



Its a normal arithmetic Progression Question , whose 1st term is 23 and common difference is -3

Tn = a+ (n-1)d

-4 = 23 +(n-1)(-3)

n = 10 .

Kudos [?]: [0], given: 1

Expert Post
1 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1810

Kudos [?]: 981 [1], given: 5

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

Show Tags

New post 11 Jan 2017, 07:09
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
enigma123 wrote:
In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = -4?

A. -1
B. 7
C. 10
D. 14
E. 20


In the given sequence, since we are given the first term, we can use that value to find the second term, and once we know the second term, we can use that value to find the third term, and so on.

t_1 = 23

t_2 = t_1 – 3 = 23 – 3 = 20

t_3 = t_2 – 3 = 20 – 3 = 17

t_4 = t_3 – 3 = 17 – 3 = 14

t_5 = t_4 – 3 = 14 – 3 = 11

t_6 = t_5 – 3 = 11 – 3 = 8

t_7 = t_6 – 3 = 8 – 3 = 5

t_8 = t_7 – 3 = 5 – 3 = 2

t_9 = t_8 – 3 = 2 – 3 = -1

t_10 = t_9 – 3 = -1 – 3 = -4

So n = 10.

Alternative Solution:

Notice that starting from the second term, each term is 3 less than the previous term, which makes the sequence an arithmetic sequence. In an arithmetic sequence, the nth term, a_n, can be found by using the formula a_n = a_1 + d(n – 1) in which a_1 is the first term and d is the common difference.

Since we are given t_n, we can modify the formula to t_n = t_1 + d(n – 1) in which t_1 = 23 and d = -3. So we have:

t_n = t_1 + d(n – 1)

-4 = 23 + (-3)(n – 1)

-27 = -3(n – 1)

9 = n – 1

10 = n

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 981 [1], given: 5

Top Contributor
Senior Manager
Senior Manager
User avatar
S
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 446

Kudos [?]: 524 [0], given: 59

Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: 337 Q168 V169
WE: Education (Education)
Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

Show Tags

New post 08 Jun 2017, 15:44
Top Contributor
Attached is a visual that should help.
Attachments

Screen Shot 2017-06-08 at 4.33.09 PM.png
Screen Shot 2017-06-08 at 4.33.09 PM.png [ 108.8 KiB | Viewed 15830 times ]


_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and online via Skype, since 2002.

GMAT Action Plan - McElroy Tutoring

Kudos [?]: 524 [0], given: 59

Intern
Intern
User avatar
B
Joined: 14 May 2016
Posts: 11

Kudos [?]: [0], given: 4

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

Show Tags

New post 05 Jul 2017, 18:18
Here is how I did it:

t1 = 23 and tn-1 = -3; therefore for every t you need to subtract 3

lets begin:

t1----> 23-3 = 20
t2----> 20-3 = 17
t3----> 17-3 = 14

when tn = 4...now subtract 4 from the 14

tn----> 14-4 = 10

Answer is C

Kudos [?]: [0], given: 4

Manager
Manager
User avatar
B
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 177

Kudos [?]: 8 [0], given: 14

Location: India
Concentration: Finance, International Business
Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

Show Tags

New post 01 Dec 2017, 19:53
i have one doubt in the question.Why cant we use the AP formula for the nth term to calculate the number if terms.When i did , i get n to be 8. Why is that method incorrect?

Kudos [?]: 8 [0], given: 14

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42620

Kudos [?]: 135707 [0], given: 12706

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

Show Tags

New post 01 Dec 2017, 22:59

Kudos [?]: 135707 [0], given: 12706

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn   [#permalink] 01 Dec 2017, 22:59
Display posts from previous: Sort by

In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.