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

It is currently 19 Jun 2019, 22:19

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

In a sequence a1, a2, …, each term after the first is found by taking

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55709
In a sequence a1, a2, …, each term after the first is found by taking  [#permalink]

Show Tags

New post 12 Jun 2019, 02:06
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

73% (01:49) correct 27% (02:17) wrong based on 15 sessions

HideShow timer Statistics

Director
Director
avatar
P
Joined: 19 Oct 2018
Posts: 503
Location: India
In a sequence a1, a2, …, each term after the first is found by taking  [#permalink]

Show Tags

New post 12 Jun 2019, 02:29
First term=\(a_1\)
Second term = \(-a_1 + 1\)
Third term = \(a_1-1+\)1=\(a_1\)
fourth term = \(-a_1+\)1
And so on

the sum of the first 99 terms= \({49*[a_1+(-a_1+1)]}+a_1\)= 49+2=51

Bunuel wrote:
In a sequence \(a_1\),\(a_2\),…, each term after the first is found by taking the negative of the preceding term, and adding 1. If \(a_1 = 2\), what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101
Senior Manager
Senior Manager
avatar
S
Joined: 22 Nov 2018
Posts: 289
Location: India
GMAT 1: 640 Q45 V35
GMAT 2: 660 Q48 V33
GMAT ToolKit User Premium Member CAT Tests
In a sequence a1, a2, …, each term after the first is found by taking  [#permalink]

Show Tags

New post Updated on: 12 Jun 2019, 21:41
Bunuel wrote:
In a sequence \(a_1\),\(a_2\),…, each term after the first is found by taking the negative of the preceding term, and adding 1. If \(a_1 = 2\), what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101


a1=2,a2=-1,a3=2,a4=-1....; So all odd values of n will be 2 and all even values will be -1; 50 Odd terms and 49 even terms; 50*2-49=51 IMO B
_________________
Give +1 kudos if this answer helps..!!

Originally posted by Arvind42 on 12 Jun 2019, 02:35.
Last edited by Arvind42 on 12 Jun 2019, 21:41, edited 1 time in total.
Director
Director
avatar
P
Joined: 19 Oct 2018
Posts: 503
Location: India
Re: In a sequence a1, a2, …, each term after the first is found by taking  [#permalink]

Show Tags

New post 12 Jun 2019, 02:37
1
1
There are 50 odd terms and 49 even terms.

Arvind42 wrote:
Bunuel wrote:
In a sequence \(a_1\),\(a_2\),…, each term after the first is found by taking the negative of the preceding term, and adding 1. If \(a_1 = 2\), what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101


a1=2,a2=-1,a3=2,a4=-1....; So all odd values of n will be 2 and all even values will be -1; 49 Odd terms and 48 even terms; 49*2-48=50 IMO B
CEO
CEO
User avatar
P
Joined: 18 Aug 2017
Posts: 3893
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: In a sequence a1, a2, …, each term after the first is found by taking  [#permalink]

Show Tags

New post 12 Jun 2019, 03:08
Bunuel wrote:
In a sequence \(a_1\),\(a_2\),…, each term after the first is found by taking the negative of the preceding term, and adding 1. If \(a_1 = 2\), what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101


from the given series we can say that odd no are 2 and even are -1
so total odd from 1 to 99 ; 50 and even ; 49
so 50*2+49*(-1) = 51
IMO C
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3785
Location: Canada
Re: In a sequence a1, a2, …, each term after the first is found by taking  [#permalink]

Show Tags

New post 12 Jun 2019, 05:35
2
Top Contributor
Bunuel wrote:
In a sequence \(a_1\),\(a_2\),…, each term after the first is found by taking the negative of the preceding term, and adding 1. If \(a_1 = 2\), what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101


Let's list some terms to get a better understanding of the desired sum.
\(a_1 = 2\)
\(a_2 = -2 + 1 = -1\)
\(a_3 = 1 + 1 = 2\)
\(a_4 = -2 + 1 = -1\)
\(a_5 = 1 + 1 = 2\)
\(a_6 = -2 + 1 = -1\)
.
.
.
We can see that all ODD numbered terms are 2, and all EVEN numbered terms are -1

From 1 to 99 inclusive, there are 50 ODD numbered terms and 49 EVEN numbered terms

So, sum = (50)(2) + (49)(-1)
= 100 + (-49)
= 51

Answer: C

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6589
Location: United States (CA)
Re: In a sequence a1, a2, …, each term after the first is found by taking  [#permalink]

Show Tags

New post 17 Jun 2019, 17:48
1
Bunuel wrote:
In a sequence \(a_1\),\(a_2\),…, each term after the first is found by taking the negative of the preceding term, and adding 1. If \(a_1 = 2\), what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101


We see that a1 = 2, a2 = -2 + 1 = -1, a3 = 1 + 1 = 2, a4 = -2 + 1 = -1 and so on.

Thus we can see that the odd-numbered terms are all 2 and the even-numbered terms are all -1. Since in the first 99 terms, there are 50 odd-numbered terms and 49 even-numbered terms, then the sum of the first 99 terms is:

50(2) + 49(-1) = 100 - 49 = 51

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: In a sequence a1, a2, …, each term after the first is found by taking   [#permalink] 17 Jun 2019, 17:48
Display posts from previous: Sort by

In a sequence a1, a2, …, each term after the first is found by taking

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


Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne