Last visit was: 23 Apr 2026, 22:28 It is currently 23 Apr 2026, 22:28
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
655-705 (Hard)|   Exponents|   Sequences|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,801
Own Kudos:
810,888
 [13]
Given Kudos: 105,867
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,801
Kudos: 810,888
 [13]
If the a-th term of a certain sequence is given by (-1)^a + (-0.1)^a 29 Jul 2019, 05:12
Kudos
Add Kudos
13
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

68% (02:35) correct 32% (02:00) wrong based on 391 sessions

History

Date
Time
Result
Not Attempted Yet
If the a-th term of a certain sequence is given by \((-1)^a + (-0.1)^a,\) then the sum of the terms from 1 to 5 is

A. -1.11111
B. -1.09091
C. 0
D. 0.90909
E. 1.11111
ShowHide Answer
Official Answer
B
User avatar
TheNightKing
User avatar
Joined: 18 Dec 2017
Last visit: 20 Mar 2024
Posts: 1,124
Own Kudos:
1,381
Given Kudos: 421
Location: United States (KS)
GMAT 1: 600 Q46 V27
GMAT 1: 600 Q46 V27
Posts: 1,124
Kudos: 1,381
If the a-th term of a certain sequence is given by (-1)^a + (-0.1)^a 29 Jul 2019, 09:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If the a-th term of a certain sequence is given by \((-1)^a + (-0.1)^a,\) then the sum of the terms from 1 to 5 is

A. -1.11111
B. -1.09091
C. 0
D. 0.90909
E. 1.11111
Show more

a=1 gives us -1-0.1 which is -1.1
a=2 gives us 1+0.1 which is 1.01
a=3 gives us -1-0.001 which is -1.001
a=4 gives us 1+0.0001 which is 1.0001
a=5 gives us -1-0.00001 which is -1.00001

Total is -1.09091.

What is the shortcut here Please?
avatar
rohitvijaysharma
avatar
Joined: 29 Jul 2019
Last visit: 19 Nov 2019
Posts: 1
Given Kudos: 4
Posts: 1
Kudos: 0
If the a-th term of a certain sequence is given by (-1)^a + (-0.1)^a 29 Jul 2019, 09:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
TheNightKing
Bunuel
If the a-th term of a certain sequence is given by \((-1)^a + (-0.1)^a,\) then the sum of the terms from 1 to 5 is

A. -1.11111
B. -1.09091
C. 0
D. 0.90909
E. 1.11111

a=1 gives us -1-0.1 which is -1.1
a=2 gives us 1+0.1 which is 1.01
a=3 gives us -1-0.001 which is -1.001
a=4 gives us 1+0.0001 which is 1.0001
a=5 gives us -1-0.00001 which is -1.00001

Total is -1.09091.

What is the shortcut here Please?
Show more

Posted from my mobile device





I think it is easier to work with huristics.

Clearly odd power implies the first for (-1) ^a terms cancel out.
The other terms are decreasing negatives with each increase in power. The first will be -0.1 and the sum of the rest will a positive decimal less than -0.1

Only answer matching such a solution is B
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 23 Apr 2026
Posts: 22,283
Own Kudos:
26,531
 [2]
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,283
Kudos: 26,531
 [2]
If the a-th term of a certain sequence is given by (-1)^a + (-0.1)^a 06 Aug 2019, 17:54
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
If the a-th term of a certain sequence is given by \((-1)^a + (-0.1)^a,\) then the sum of the terms from 1 to 5 is

A. -1.11111
B. -1.09091
C. 0
D. 0.90909
E. 1.11111
Show more

When a is 1:

-1 + (-0.1)

When a is 2:

1 + 0.01

When a is 3:

-1 + (-0.001)

When a is 4:

1 + (0.0001)

When a is 5:

-1 + (-0.00001)

We see that the sum of integer parts of the first 5 terms is:

-1 + 1 + (-1) + 1 + (-1) = -1

And the sum of the decimal parts of the first 5 terms is:

-0.1 + 0.01 + (-0.001) + 0.0001 + (-0.00001) = -0.09 + (-0.0009) + (-0.00001) = -0.09091

Therefore, the sum of the first 5 terms is:

-1 + (-0.09091) = -1.09091

Answer: B
User avatar
SaquibHGMATWhiz
User avatar
GMATWhiz Representative
Joined: 23 May 2022
Last visit: 12 Jun 2024
Posts: 623
Own Kudos:
777
Given Kudos: 6
Location: India
GMAT 1: 760 Q51 V40
Expert
Expert reply
GMAT 1: 760 Q51 V40
Posts: 623
Kudos: 777
If the a-th term of a certain sequence is given by (-1)^a + (-0.1)^a 01 Mar 2023, 03:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If the a-th term of a certain sequence is given by \((-1)^a + (-0.1)^a,\) then the sum of the terms from 1 to 5 is

A. -1.11111
B. -1.09091
C. 0
D. 0.90909
E. 1.11111
Show more
Solution:

  • First Term
  • \((-1)^a=(-1)^1+(-1)^2+(-1)^3+(-1)^4+(-1)^5=-1+1-1+1-1=-1\)

  • Second Term
  • \((-0.1)^a=(-0.1)^1+(-0.1)^2+(-0.1)^3+(-0.1)^4+(-0.1)^5=-0.1+0.01-0.001+0.0001-0.00001=-0.09091\)

  • Adding them, we get \(-1-0.09091=-1.09091\)

Hence the right answer is Option B
Moderators:
Bunuel
Math Expert
109795 posts
Krunaal
Tuck School Moderator
853 posts