Last visit was: 16 Jul 2024, 11:57 It is currently 16 Jul 2024, 11:57
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# Each term of a certain sequence is 3 less than the previous term. The

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 04 Aug 2013
Posts: 81
Own Kudos [?]: 1058 [20]
Given Kudos: 56
Location: India
Schools: McCombs '17
GMAT 1: 670 Q47 V35
GPA: 3
WE:Manufacturing and Production (Pharmaceuticals and Biotech)
Math Expert
Joined: 02 Sep 2009
Posts: 94370
Own Kudos [?]: 641390 [10]
Given Kudos: 85332
General Discussion
Tutor
Joined: 16 Oct 2010
Posts: 15114
Own Kudos [?]: 66668 [2]
Given Kudos: 436
Location: Pune, India
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1558
Own Kudos [?]: 7292 [0]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Re: Each term of a certain sequence is 3 less than the previous term. The [#permalink]
19 .... 16.... 13 .......... 10 ......... 7.......... 4.......... 1 .......... -2 .......... -5 .......... -8 ........... -11 .......... -14............. -17

6 terms to the left of 1

6 terms to the right of 1

Total = 6+6+1 = 13

Corresponding terms addition = 4-2 = 7-5 = 10-8 = 2 .......... so on

Total = 1 + 2*6 = 13

Board of Directors
Joined: 17 Jul 2014
Posts: 2145
Own Kudos [?]: 1190 [0]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Re: Each term of a certain sequence is 3 less than the previous term. The [#permalink]
anceer wrote:
Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 19. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?

A 1
B 13
C 15
D 19
E 47

this one can be solved logically as well..
1 definitely can't be
47 as well..as it would be way to down in the negative side..and thus n can't be negative.

now..
19, 16, 13, 10, 7, 4, 1, -2, -5, -8, -11, -14, -17, -20, -23... list all these numbers..to go further is pointless as the sum would be negative...
19-17=2
16-14=2
13-11=2
10-8=2
7-5=2
4-2=2
1
add these up = 13.
13 numbers, sum is 13. so B it is.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19147
Own Kudos [?]: 22646 [2]
Given Kudos: 286
Location: United States (CA)
Re: Each term of a certain sequence is 3 less than the previous term. The [#permalink]
2
Kudos
anceer wrote:
Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 19. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?

A 1
B 13
C 15
D 19
E 47

We have an arithmetic sequence, which has a general formula for the nth term as: a(n) = a(1) + d*(n - 1), where a(1) is the first term and d is the common difference. In this question, a(1) = 19 and d = -3.

We can let a(1) = 19, a(2) = 16, a(3) = 13 and so on. Therefore, the nth term, a(n) = 19 - 3*(n - 1) = 22 - 3n. Since the sequence is evenly spaced, we can use the formula: sum = average x quantity. Since the average of a finite evenly spaced sequence of n terms is [a(1) + a(n)] / 2, we have:

n = ([a(1) + a(n)] / 2) x n

n = ([19 + 22 - 3n] / 2) x n

1 = (41 - 3n) / 2

2 = 41 - 3n

3n = 39

n = 13

Non-Human User
Joined: 09 Sep 2013
Posts: 33991
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: Each term of a certain sequence is 3 less than the previous term. The [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: Each term of a certain sequence is 3 less than the previous term. The [#permalink]
Moderator:
Math Expert
94370 posts