Last visit was: 11 Jul 2025, 08:55 It is currently 11 Jul 2025, 08:55
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
Sub 505 Level|   Sequences|                     
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,634
Own Kudos:
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,634
Kudos: 740,417
 [24]
5
Kudos
Add Kudos
19
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,634
Own Kudos:
740,417
 [4]
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,634
Kudos: 740,417
 [4]
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
User avatar
WoundedTiger
Joined: 25 Apr 2012
Last visit: 25 Sep 2024
Posts: 523
Own Kudos:
2,479
 [4]
Given Kudos: 740
Location: India
GPA: 3.21
WE:Business Development (Other)
Products:
Posts: 523
Kudos: 2,479
 [4]
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
avatar
AKG1593
Joined: 20 Dec 2013
Last visit: 30 Mar 2024
Posts: 182
Own Kudos:
312
 [1]
Given Kudos: 35
Location: India
Posts: 182
Kudos: 312
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ans.C
This is nothing but an AP with common diff=5
a5=31,
a4=26
a3=21,
a2=16,
a1=11

a5=a1+4d
31=a1+4*5
31-20=a1=11
User avatar
vikrantgulia
Joined: 18 Oct 2013
Last visit: 23 Oct 2022
Posts: 62
Own Kudos:
306
 [3]
Given Kudos: 36
Location: India
Concentration: Technology, Finance
GMAT 1: 580 Q48 V21
GMAT 2: 530 Q49 V13
GMAT 3: 590 Q49 V21
WE:Information Technology (Computer Software)
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
This answer can be easily be solve by A.P.
The sequence is an A.P. with each term at an increment of 5 from the previous term.
So a5 is nothing but a1+20.

a5=a1+20=31
=> a1=11.

Answer is C
User avatar
arunspanda
Joined: 04 Oct 2013
Last visit: 31 Oct 2021
Posts: 127
Own Kudos:
321
 [4]
Given Kudos: 55
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Products:
Posts: 127
Kudos: 321
 [4]
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
The sequence \(a_1, a_2, a_3, a_4, a_5\) is such that \(a_n= a_{n-1} + 5\) for \(2\leq n \leq 5\). If \(a_5 = 31\), what is the value of \(a_1\) ?

(A) 1
(B) 6
(C) 11
(D) 16
(E) 21


Given sequence is A.P. with common difference of 5.
Last Term - First Term = (Number of terms -1)* common difference

\(a_5-a_1 = (5-1)*\) \(common\) \(difference\)

Or, \(31-a_1=(5-1)*5\)

Or, \(a_1=31-20=11\)

Answer: (C)
avatar
havoc7860
Joined: 21 Oct 2012
Last visit: 12 Jan 2015
Posts: 27
Own Kudos:
66
 [1]
Given Kudos: 19
Location: United States
Concentration: Marketing, Operations
GMAT 1: 650 Q44 V35
GMAT 2: 600 Q47 V26
GMAT 3: 660 Q43 V38
GPA: 3.6
WE:Information Technology (Computer Software)
GMAT 3: 660 Q43 V38
Posts: 27
Kudos: 66
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
SOLUTION

The sequence \(a_1\), \(a_2\), \(a_3\), \(a_4\), \(a_5\) is such that \(a_n= a_{n-1} + 5\) for \(2\leq n \leq 5\). If \(a_5 = 31\), what is the value of \(a_1\) ?

(A) 1
(B) 6
(C) 11
(D) 16
(E) 21

\(a_5 = 31\);
\(a_4 =31-5=26\);
\(a_3 =26-5=21\);
\(a_2 =21-5=16\);
\(a_1 =16-5=1\).

Answer: C.


But 2<= n <= 5 so how is this applicable to a1 i.e. n=1?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,634
Own Kudos:
740,417
 [2]
Given Kudos: 98,170
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,634
Kudos: 740,417
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
havoc7860
Bunuel
SOLUTION

The sequence \(a_1\), \(a_2\), \(a_3\), \(a_4\), \(a_5\) is such that \(a_n= a_{n-1} + 5\) for \(2\leq n \leq 5\). If \(a_5 = 31\), what is the value of \(a_1\) ?

(A) 1
(B) 6
(C) 11
(D) 16
(E) 21

\(a_5 = 31\);
\(a_4 =31-5=26\);
\(a_3 =26-5=21\);
\(a_2 =21-5=16\);
\(a_1 =16-5=1\).

Answer: C.


But 2<= n <= 5 so how is this applicable to a1 i.e. n=1?

\(a_n= a_{n-1} + 5\) --> for n=2, we get: \(a_2= a_{1} + 5\).

Hope it helps.
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,996
Own Kudos:
7,922
 [1]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,996
Kudos: 7,922
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:

The sequence \(a_1\), \(a_2\), \(a_3\), \(a_4\), \(a_5\) is such that \(a_n= a_{n-1} + 5\) for \(2\leq n \leq 5\). If \(a_5 = 31\), what is the value of \(a_1\) ?

(A) 1
(B) 6
(C) 11
(D) 16
(E) 21

a(5) = 31, so:

a(5) = a(4) + 5

31 = a(4) + 5

26 = a(4)

The pattern is to subtract 5 to obtain the value of the previous term in this recursively-defined sequence.

Thus, a(3) = 21, a(2) =16, and a(1) = 11.

Answer: C
User avatar
ArnauG
Joined: 23 Dec 2022
Last visit: 14 Oct 2023
Posts: 301
Own Kudos:
Given Kudos: 199
Posts: 301
Kudos: 42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
To find the value of a1, we can work backward from the given information and use the recursive formula provided.

Given that a5 = 31 and the recursive formula is an = an−1 + 5, we can calculate the preceding terms in the sequence until we reach a1.

Starting from a5 = 31:
a4 = a5 - 5 = 31 - 5 = 26
a3 = a4 - 5 = 26 - 5 = 21
a2 = a3 - 5 = 21 - 5 = 16
a1 = a2 - 5 = 16 - 5 = 11

Therefore, the value of a1 is 11.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,371
Own Kudos:
Posts: 37,371
Kudos: 1,010
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Math Expert
102634 posts
PS Forum Moderator
686 posts