Author 
Message 
TAGS:

Hide Tags

Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 511
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn
[#permalink]
Show Tags
20 Mar 2012, 09:00
Question Stats:
79% (01:14) correct 21% (01:08) wrong based on 762 sessions
HideShow timer Statistics
In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn1  3 for each n > 1. What is the value of n when tn = 4? A. 1 B. 7 C. 10 D. 14 E. 20
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730




Math Expert
Joined: 02 Sep 2009
Posts: 47161

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn
[#permalink]
Show Tags
20 Mar 2012, 13:44
enigma123 wrote: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn1  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? \(t_n=t_{n1}3\) 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? Extrahard Quant Tests with Brilliant Analytics




Senior Manager
Joined: 23 Oct 2010
Posts: 364
Location: Azerbaijan
Concentration: Finance

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn
[#permalink]
Show Tags
12 Apr 2012, 10:24
tn= tn1  3 means that d=3 tn=t1 +d(n1) 4=233(n1) 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




Intern
Joined: 04 Feb 2012
Posts: 6
Location: Greece
Concentration: Entrepreneurship, General Management
GMAT Date: 03072012
WE: General Management (Real Estate)

Re: Arithmetic Sequence
[#permalink]
Show Tags
20 Mar 2012, 09:42
well.....t 2 =t 13 =233=20 t 3=t 23=203=17 So every time we n increases tn decreases by 3. Since t 1=23 we have 233=203=173=143=113=83=53=23=13=4!VOILA So n=10 ten times substructing 3 from 23 to reach 4. clear



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
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
22 Apr 2014, 02:15
23... 20.... 17... 14... 11.... 8... 5... 2.... 1.... 44 is the 10th term Answer = 10
_________________
Kindly press "+1 Kudos" to appreciate



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 423
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn
[#permalink]
Show Tags
03 Feb 2015, 01:44
I also did the same as Paresh, but like this:
We know that t1 = 23 So, using the given formula we have: t1=(t11) 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..



Intern
Joined: 22 Jul 2016
Posts: 24

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn
[#permalink]
Show Tags
09 Jan 2017, 00:59
t1=23 t2=t13=20 t3=t23=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(n1)
given, tn=4 4=23 + (3) (n10) >> n=10
Ans : C



Intern
Joined: 07 Sep 2016
Posts: 6

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn
[#permalink]
Show Tags
09 Jan 2017, 03:17
enigma123 wrote: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn1  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+ (n1)d 4 = 23 +(n1)(3) n = 10 .



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2679

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn
[#permalink]
Show Tags
11 Jan 2017, 08:09
enigma123 wrote: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn1  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 SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 657
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
WE: Education (Education)

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn
[#permalink]
Show Tags
08 Jun 2017, 16:44
Attached is a visual that should help.
Attachments
Screen Shot 20170608 at 4.33.09 PM.png [ 108.8 KiB  Viewed 40990 times ]
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both inperson (San Diego, CA, USA) and online worldwide, since 2002.
One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).
You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y94hlarr Date of Birth: 09 December 1979.
GMAT Action Plan and Free EBook  McElroy Tutoring
Contact: mcelroy@post.harvard.edu



Intern
Joined: 14 May 2016
Posts: 24

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn
[#permalink]
Show Tags
05 Jul 2017, 19:18
Here is how I did it:
t1 = 23 and tn1 = 3; therefore for every t you need to subtract 3
lets begin:
t1> 233 = 20 t2> 203 = 17 t3> 173 = 14
when tn = 4...now subtract 4 from the 14
tn> 144 = 10
Answer is C



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12004
Location: United States (CA)

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn
[#permalink]
Show Tags
28 Feb 2018, 22:41
Hi All, Questions that use "sequence notation" are relatively rare on Test Day (you'll probably see just 1), but the math behind the sequence is usually some fairly simple arithmetic (add, subtract, multiply, divide). Here, we're given the first term in the sequence (23) and we're told that each term thereafter is 3 LESS than the preceding term. Once you understand how the sequence "works", in many cases, it's really easy to just "map out" the sequence. We're asked which term in the sequence equals 4..... 1st = 23 2nd = 20 3rd = 17 4th = 14 5th = 11 6th = 8 7th = 5 8th = 2 9th = 1 10th = 4 Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Intern
Joined: 07 May 2018
Posts: 2

In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn
[#permalink]
Show Tags
07 May 2018, 12:41
a sequence of numbers contains terms t1, t2, t3,......... , tn, where every term is equal to the sum of its two preceding terms. t5 =18 and t8 = 76 what is the value of t9
Answer this



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12004
Location: United States (CA)

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn
[#permalink]
Show Tags
07 May 2018, 16:12
Hi Mangalshubham, In the future, when posting questions, you should post each in its own unique thread AND you should make sure to post the ENTIRE prompt (with the 5 answer choices and the correct answer  hidden behind a "spoiler" tag). The prompt you've submitted is a sequence question that you can use to create the following equations. We're told that each term is equal to the SUM of the TWO terms that immediately precede it... 5th term = 18 6th term = X 7th term = 18+X 8th term = 76 = (X + 18 + X) 76 = 2X + 18 58 = 2X 29 = X Thus, we have... 5th term = 18 6th term = 29 7th term = 47 8th term = 76 9th term = ? Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Intern
Joined: 07 May 2018
Posts: 2

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn
[#permalink]
Show Tags
07 May 2018, 21:10
Empower GmatRich Thank you for solution... and this question doen not have answer choices.. it is weather the 9th term is equal or less than 126 Posted from my mobile device




Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn &nbs
[#permalink]
07 May 2018, 21:10






