Last visit was: 23 Apr 2026, 12:13 It is currently 23 Apr 2026, 12:13
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
605-655 (Medium)|   Algebra|   Sequences|      
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,871
 [46]
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,871
 [46]
In the sequence S, the difference between any two consecutive terms is Updated on: 07 Aug 2018, 21:24
Originally posted by EgmatQuantExpert on 23 May 2017, 07:03.
Last edited by EgmatQuantExpert on 07 Aug 2018, 21:24, edited 1 time in total.
4
Kudos
Add Kudos
42
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:

45% (medium)

Question Stats:

68% (01:54) correct 32% (02:18) wrong based on 1039 sessions

History

Date
Time
Result
Not Attempted Yet
In the sequence S, the difference between any two consecutive terms is equal. If the sum of the fourth term and the fifth term of the sequence is equal to the seventh term of the sequence, what is the value of the second term of the sequence?

    A. -4
    B. 0
    C. 4
    D. 8
    E. Cannot be Determined

Thanks,
Saquib
Quant Expert
e-GMAT

To read all our articles: Must read articles to reach Q51

ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
quantumliner
User avatar
Joined: 24 Apr 2016
Last visit: 26 Sep 2018
Posts: 240
Own Kudos:
804
 [13]
Given Kudos: 48
Posts: 240
Kudos: 804
 [13]
In the sequence S, the difference between any two consecutive terms is 23 May 2017, 08:43
8
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
Let the first seven terms be denoted as below
a,a+d,a+2d,a+3d,a+4d,a+5d,a+6d

Now,
a+3d+a+4d=a+6d
a=-d

So second term = d-d = 0

Answer is B. 0
General Discussion
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,871
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,871
In the sequence S, the difference between any two consecutive terms is Updated on: 31 May 2017, 04:44
Originally posted by EgmatQuantExpert on 23 May 2017, 07:03.
Last edited by EgmatQuantExpert on 31 May 2017, 04:44, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The official solution has been posted. Looking forward to a healthy discussion..:)
User avatar
attari92
User avatar
Joined: 25 Apr 2016
Last visit: 28 May 2019
Posts: 56
Own Kudos:
42
 [1]
Given Kudos: 308
Posts: 56
Kudos: 42
 [1]
In the sequence S, the difference between any two consecutive terms is 23 May 2017, 07:09
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
the sequence is in AP and the second term would be 1st term plus the common difference. Now,2a +7d = a+6d => a+ d = 0 -> option B
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,871
 [3]
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,871
 [3]
In the sequence S, the difference between any two consecutive terms is Updated on: 07 Aug 2018, 21:26
Originally posted by EgmatQuantExpert on 31 May 2017, 04:44.
Last edited by EgmatQuantExpert on 07 Aug 2018, 21:26, edited 1 time in total.
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post

Official Solution




Given


    • In a sequence S, difference between any two terms is equal

      o S is an arithmetic sequence
      o Let the first term of the sequence be a and the common difference be d

    • 4th   term + 5th  term = 7th  term

      o 4th  term = a + (4-1)*d = a+ 3d
      o 5th  term = a + (5-1)*d = a +4d
      o 7th term = a + (7-1)d = a + 6d

To Find: a + d = ?


Working Out

    • (a + 3d) + (a+4d) = a+ 6d

      o 2a + 7d = a + 6d

      o a + d = 0

    • Hence, the value of the 2nd term of the sequence = a + d = 0



Answer: B

Thanks,
Saquib
Quant Expert
e-GMAT

avatar
matt882
avatar
Joined: 08 Dec 2016
Last visit: 18 Sep 2020
Posts: 25
Own Kudos:
36
Given Kudos: 559
Location: Italy
Schools: IESE '21
Schools: IESE '21
Posts: 25
Kudos: 36
In the sequence S, the difference between any two consecutive terms is 20 Jun 2017, 15:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
a, a+d, a+2d, a+3d, a+4d, a+5d, a+6d, a+7d.

a4= a7-a5 = 2d

Therefore:
a2= a4 - d - d= 0

Thanks,
Matt
User avatar
rekhabishop
User avatar
Joined: 22 Sep 2016
Last visit: 18 May 2018
Posts: 129
Own Kudos:
80
 [2]
Given Kudos: 42
Location: India
Schools: Degroote McMaster"19 (A$) HBS '20 (D) Stanford '20 (D) Wharton '20 (D) Booth '20 (D) Kellogg '20 Haas '20
GMAT 1: 710 Q50 V35
GPA: 4
Schools: Degroote McMaster"19 (A$) HBS '20 (D) Stanford '20 (D) Wharton '20 (D) Booth '20 (D) Kellogg '20 Haas '20
GMAT 1: 710 Q50 V35
Posts: 129
Kudos: 80
 [2]
In the sequence S, the difference between any two consecutive terms is 14 Jul 2017, 02:00
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EgmatQuantExpert
In the sequence S, the difference between any two consecutive terms is equal. If the sum of the fourth term and the fifth term of the sequence is equal to the seventh term of the sequence, what is the value of the second term of the sequence?

    A. -4
    B. 0
    C. 4
    D. 8
    E. Cannot be Determined

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

Show more

A very easy question!

Use concept of AP.

a+3d + a+4d = a+6d

a+d = 0
avatar
FB2017
avatar
Joined: 18 Jun 2017
Last visit: 14 Sep 2017
Posts: 50
Own Kudos:
14
Given Kudos: 165
Posts: 50
Kudos: 14
In the sequence S, the difference between any two consecutive terms is 07 Aug 2017, 00:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
a+3d+a+4d=a+6d [From problem statement]
a+d=0 -> This would be the 2nd term of the series.
Option B.
User avatar
gracie
User avatar
Joined: 07 Dec 2014
Last visit: 11 Oct 2020
Posts: 1,028
Own Kudos:
2,021
Given Kudos: 27
Posts: 1,028
Kudos: 2,021
In the sequence S, the difference between any two consecutive terms is 07 Aug 2017, 22:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EgmatQuantExpert
In the sequence S, the difference between any two consecutive terms is equal. If the sum of the fourth term and the fifth term of the sequence is equal to the seventh term of the sequence, what is the value of the second term of the sequence?

A. -4
B. 0
C. 4
D. 8
E. Cannot be Determined
Show more

let x+3=fourth term
x+4=fifth term
x+6=seventh term
adding, 2x+7=x+6➡
x=-1=first term
sequence=-1,0,1,2,3,4,5..
second term=0
B
User avatar
luisdicampo
User avatar
Joined: 10 Feb 2025
Last visit: 19 Apr 2026
Posts: 480
Own Kudos:
73
Given Kudos: 328
Products:
My Reviews Forum Quiz
Posts: 480
Kudos: 73
In the sequence S, the difference between any two consecutive terms is 16 Apr 2026, 05:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Deconstructing the Question

Since the difference between consecutive terms is constant, the sequence is arithmetic.

Let the first term be \(a\) and the common difference be \(d\).

Then the \(n\)th term is

\(T_n=a+(n-1)d\)

We are given that

\(T_4+T_5=T_7\)

and we need to find \(T_2\).

Step-by-step

Write the relevant terms:

\(T_4=a+3d\)

\(T_5=a+4d\)

\(T_7=a+6d\)

Use the condition:

\((a+3d)+(a+4d)=a+6d\)

Simplify:

\(2a+7d=a+6d\)

\(a+d=0\)

But

\(T_2=a+d\)

So

\(T_2=0\)

Answer: B
Moderators:
Bunuel
Math Expert
109783 posts
Krunaal
Tuck School Moderator
853 posts