Last visit was: 03 Sep 2026, 04:34 It is currently 03 Sep 2026, 04:34
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
805+ (Hard)|   Sequences|      
User avatar
devashish2407
User avatar
Joined: 28 Jul 2022
Last visit: 06 Sep 2025
Posts: 58
Own Kudos:
106
 [14]
Given Kudos: 139
Posts: 58
Kudos: 106
 [14]
After the first term in a finite sequence of numbers, each even-number 02 Apr 2024, 03:45
1
Kudos
Add Kudos
13
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

48% (02:38) correct 52% (02:58) wrong based on 275 sessions

History

Date
Time
Result
Not Attempted Yet
After the first term in a finite sequence of numbers, each even-numbered term is created by adding 3 to the previous term, and each odd-numbered term is created by multiplying the previous term by –1. How many terms are in the sequence?

(1) The average of all terms in the sequence is \(-\frac{1}{2}\).
(2) The eighteenth term in the sequence is \(–4\).
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
gmatophobia
User avatar
Quant Chat Moderator
Joined: 22 Dec 2016
Last visit: 30 Aug 2026
Posts: 3,174
Own Kudos:
12,307
 [6]
Given Kudos: 1,860
Location: India
Concentration: Strategy, Leadership
Posts: 3,174
Kudos: 12,307
 [6]
After the first term in a finite sequence of numbers, each even-number 03 Apr 2024, 23:47
6
Kudos
Add Kudos
Bookmarks
Bookmark this Post
devashish2407
After the first term in a finite sequence of numbers, each even-numbered term is created by adding 3 to the previous term, and each odd-numbered term is created by multiplying the previous term by –1. How many terms are in the sequence? 



  1. The average of all terms in the sequence is \(\frac{-1}{2}.\)
  2. The eighteenth term in the sequence is \(–4.\)



 
Show more
­Assume that the first number in the series is equal to x 

We can write that series as shown below 

 ­
Attachment:
Screenshot 2024-04-04 120443.png
Screenshot 2024-04-04 120443.png [ 50.14 KiB | Viewed 3214 times ]

Observation: In every block of 4, the sum of the terms in the block = 0­

Statement 1

The average of all terms in the sequence is \(\frac{-1}{2}.\)

This statement alone doesn't help much. As the value of x is unknown, for a particular value of x we can obtain a given average. 

Example: If the number of terms = 5

Average =\(\frac{ \text{The sum of the first five terms} }{ \text{Number of terms}} \)­

\(\frac{-1}{2}=\frac{ \text{The sum of the first five terms} }{ \text{Number of terms}} \)­

\(\frac{-1}{2}=\frac{ x }{ 5} \)­

\(x = \frac{-5}{2}\)

Hence, when \(x = \frac{-5}{2}\); the number of terms = 5

​​​​​​​Example: If the number of terms = 3

Average =\(\frac{ \text{The sum of the first three terms} }{ \text{Number of terms}} \)­

\(\frac{-1}{2}=\frac{ \text{The sum of the first three terms} }{ \text{Number of terms}} \)­

\(\frac{-1}{2}=\frac{ x }{ 3} \)­

\(​​​​​​​x = \frac{-3}{2}\)

Hence, when \(​​​​​​​x = \frac{-3}{2}\); the number of terms = 3­

This statement alone is not sufficient to answer the question. We can eliminate A, and D.

Statement 2

The eighteenth term in the sequence is \(–4.\)

Statement 2 alone is not sufficient. We know the value of the 18th term, however we do not know the number of terms in the sequence.

Eliminate B

Combined

From Statement 2, we can get a unique value of x. 

The 18th term of the sequence = x + 3

x + 3 = -4

x = -7

From Statement 1, we know that for any unique value of x, we can find the number of terms. 

As the value of x is now known, we can obtain the number of terms in the sequence. 

The statements combined are sufficient to answer the question asked. 

Option C
General Discussion
User avatar
Guntabulla
User avatar
Joined: 24 Jul 2023
Last visit: 30 Jan 2026
Posts: 23
Own Kudos:
93
 [1]
Given Kudos: 16
Location: India
Schools: ISB '26 (A$)
GPA: 9
Schools: ISB '26 (A$)
Posts: 23
Kudos: 93
 [1]
After the first term in a finite sequence of numbers, each even-number 13 May 2024, 00:35
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatophobia

devashish2407
After the first term in a finite sequence of numbers, each even-numbered term is created by adding 3 to the previous term, and each odd-numbered term is created by multiplying the previous term by –1. How many terms are in the sequence? 




  1. The average of all terms in the sequence is \(\frac{-1}{2}.\)
  2. The eighteenth term in the sequence is \(–4.\)




 
­Assume that the first number in the series is equal to x 

We can write that series as shown below 

 ­
Attachment:
Screenshot 2024-04-04 120443.png

Observation: In every block of 4, the sum of the terms in the block = 0­

Statement 1

The average of all terms in the sequence is \(\frac{-1}{2}.\)

This statement alone doesn't help much. As the value of x is unknown, for a particular value of x we can obtain a given average. 

Example: If the number of terms = 5

Average =\(\frac{ \text{The sum of the first five terms} }{ \text{Number of terms}} \)­

\(\frac{-1}{2}=\frac{ \text{The sum of the first five terms} }{ \text{Number of terms}} \)­

\(\frac{-1}{2}=\frac{ x }{ 5} \)­

\(x = \frac{-5}{2}\)

Hence, when \(x = \frac{-5}{2}\); the number of terms = 5

Example: If the number of terms = 3

Average =\(\frac{ \text{The sum of the first three terms} }{ \text{Number of terms}} \)­

\(\frac{-1}{2}=\frac{ \text{The sum of the first three terms} }{ \text{Number of terms}} \)­

\(\frac{-1}{2}=\frac{ x }{ 3} \)­

\(​​​​​​​x = \frac{-3}{2}\)

Hence, when \(​​​​​​​x = \frac{-3}{2}\); the number of terms = 3­

This statement alone is not sufficient to answer the question. We can eliminate A, and D.

Statement 2

The eighteenth term in the sequence is \(–4.\)

Statement 2 alone is not sufficient. We know the value of the 18th term, however we do not know the number of terms in the sequence.

Eliminate B

Combined

From Statement 2, we can get a unique value of x. 

The 18th term of the sequence = x + 3

x + 3 = -4

x = -7

From Statement 1, we know that for any unique value of x, we can find the number of terms. 

As the value of x is now known, we can obtain the number of terms in the sequence. 

The statements combined are sufficient to answer the question asked. 

Option C
Show more
­From Statement 2 we only find out the first term of the sequence right?

So how do we know what the number of terms are?

For example if the sum is -7 then n will be 14
if the sum is -11 then n will be 22

Arent there multiple values n can take?
User avatar
dibz101
User avatar
Joined: 16 Aug 2023
Last visit: 03 May 2025
Posts: 8
Given Kudos: 8
Location: India
Schools: Haas '27 (I) Anderson '27 Columbia '27
GMAT Focus 1: 675 Q90 V81 DI79
GPA: 3.3
Schools: Haas '27 (I) Anderson '27 Columbia '27
GMAT Focus 1: 675 Q90 V81 DI79
Posts: 8
Kudos: 0
After the first term in a finite sequence of numbers, each even-number 01 Jun 2024, 04:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
It's not clear how the number of elements can be obtained by just knowing the value of the 17th term and knowing the average of the series is -1/2
User avatar
Samya2113
User avatar
Joined: 23 May 2024
Last visit: 28 Oct 2025
Posts: 4
Own Kudos:
4
 [1]
Given Kudos: 79
GMAT Focus 1: 655 Q83 V83 DI81
GMAT Focus 1: 655 Q83 V83 DI81
Posts: 4
Kudos: 4
 [1]
After the first term in a finite sequence of numbers, each even-number 22 Jul 2024, 07:16
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatophobia
­Assume that the first number in the series is equal to x

We can write that series as shown below

­
Attachment:
Screenshot 2024-04-04 120443.png

Observation: In every block of 4, the sum of the terms in the block = 0­

Statement 1

The average of all terms in the sequence is \(\frac{-1}{2}.\)

This statement alone doesn't help much. As the value of x is unknown, for a particular value of x we can obtain a given average.

Example: If the number of terms = 5

Average =\(\frac{ \text{The sum of the first five terms} }{ \text{Number of terms}} \)­

\(\frac{-1}{2}=\frac{ \text{The sum of the first five terms} }{ \text{Number of terms}} \)­

\(\frac{-1}{2}=\frac{ x }{ 5} \)­

\(x = \frac{-5}{2}\)

Hence, when \(x = \frac{-5}{2}\); the number of terms = 5

Example: If the number of terms = 3

Average =\(\frac{ \text{The sum of the first three terms} }{ \text{Number of terms}} \)­

\(\frac{-1}{2}=\frac{ \text{The sum of the first three terms} }{ \text{Number of terms}} \)­

\(\frac{-1}{2}=\frac{ x }{ 3} \)­

\(​​​​​​​x = \frac{-3}{2}\)

Hence, when \(​​​​​​​x = \frac{-3}{2}\); the number of terms = 3­

This statement alone is not sufficient to answer the question. We can eliminate A, and D.

Statement 2

The eighteenth term in the sequence is \(–4.\)

Statement 2 alone is not sufficient. We know the value of the 18th term, however we do not know the number of terms in the sequence.

Eliminate B

Combined

From Statement 2, we can get a unique value of x.

The 18th term of the sequence = x + 3

x + 3 = -4

x = -7

From Statement 1, we know that for any unique value of x, we can find the number of terms.

As the value of x is now known, we can obtain the number of terms in the sequence.

The statements combined are sufficient to answer the question asked.

Option C
Show more
Hi gmatophobia
­So let's say we have our first term x = -7, from which we can deduce the number of terms which is 14.
let's try to validate this...
for 14 terms, sum of those terms S = -7 + (-7+3) = -11
average = -11/14
this is not equal to -1/2 as specified in the options

How can we say that both the statements are sufficient?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 03 Sep 2026
Posts: 113,078
Own Kudos:
838,799
Given Kudos: 111,297
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,078
Kudos: 838,799
After the first term in a finite sequence of numbers, each even-number 22 Jul 2024, 08:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Samya2113
After the first term in a finite sequence of numbers, each even-numbered term is created by adding 3 to the previous term, and each odd-numbered term is created by multiplying the previous term by –1. How many terms are in the sequence?

(1) The average of all terms in the sequence is \(-\frac{1}{2}\).
(2) The eighteenth term in the sequence is \(–4\).


Hi gmatophobia
­So let's say we have our first term x = -7, from which we can deduce the number of terms which is 14.
let's try to validate this...
for 14 terms, sum of those terms S = -7 + (-7+3) = -11
average = -11/14
this is not equal to -1/2 as specified in the options

How can we say that both the statements are sufficient?
Show more
­
When we combine the statements we get that the the sequence is:

-7, -4, 4, 7, -7, -4, 4, 7, -7, -4, 4, 7, -7, -4, 4, 7, -7, -4, 4, 7, ...

The sum of the terms is thus (for 1, 2, 3, ... and so on terms):

-7, -11, -7, 0, -7, -11, -7, 0, -7, -11, -7, 0, -7, -11, -7, 0, -7, -11, -7, 0,
______________________________

From (1) we know that (sum of the terms)/(number of the terms) = -1/2, so:

(sum of the terms) = -1/2 * (number of the terms)
The sum of the terms is thus (for 1, 2, 3, ... and so on terms):

-1/2, -2/2, -3/2, -4/2, -5/2, -6/2, -7/2, -8/2, ...
______________________________
The corresponding numbers in the red and green lists will coincide once at n = 22.
­
User avatar
pizzapalooza
User avatar
Joined: 28 Feb 2026
Last visit: 03 Sep 2026
Posts: 7
Given Kudos: 148
GMAT Focus 1: 675 Q86 V82 DI83
Products:
My Reviews GMAT Club Tests Forum Quiz
GMAT Focus 1: 675 Q86 V82 DI83
Posts: 7
Kudos: 0
After the first term in a finite sequence of numbers, each even-number 10 Aug 2026, 03:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Maybe this'll help:

1st term: x
2nd: x + 3
3rd: -x-3
4th: -x
5th: x again

Hence sum of every 4 terms is 0, Look at the cyclicity of 4.

Now when we take both statements together,
We know sum of 1st term: -7
1st + 2nd term: -11
1st + 2nd + 3rd: -7
1st + 2nd + 3rd + 4th: 0

We're given that sum/n = -1/2
i.e. sum = -n/2

Hence n has to be a a number such that -n/2 is a number out of our possible list of sums.
If we take -7. Here n would have to be 14. But at n=14, sum would be 1st + 2nd term i.e. -7 (after exhausting 3 cycles of 4 terms)
If we take sum as -11. Here n would be 22. At n=22, I would indeed get sum of 1st + 2nd term as -11 itself. Hence, this is the answer.

devashish2407
After the first term in a finite sequence of numbers, each even-numbered term is created by adding 3 to the previous term, and each odd-numbered term is created by multiplying the previous term by –1. How many terms are in the sequence?

(1) The average of all terms in the sequence is \(-\frac{1}{2}\).
(2) The eighteenth term in the sequence is \(–4\).
Show more
User avatar
pizzapalooza
User avatar
Joined: 28 Feb 2026
Last visit: 03 Sep 2026
Posts: 7
Given Kudos: 148
GMAT Focus 1: 675 Q86 V82 DI83
Products:
My Reviews GMAT Club Tests Forum Quiz
GMAT Focus 1: 675 Q86 V82 DI83
Posts: 7
Kudos: 0
After the first term in a finite sequence of numbers, each even-number 10 Aug 2026, 07:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1st term: x
2nd: x + 3
3rd: -x-3
4th: -x
5th: x again


Hence sum of every 4 terms is 0, Look at the cyclicity of 4.


Now when we take both statements together,
We know sum of 1st term: -7
1st + 2nd term: -11
1st + 2nd + 3rd: -7
1st + 2nd + 3rd + 4th: 0


We're given that sum/n = -1/2
i.e. sum = -n/2


Hence n has to be a number such that -n/2 is a number out of our possible list of sums.
If we take -7. Here n would have to be 14. But at n=14, sum would be 1st + 2nd term i.e. -7 (after exhausting 3 cycles of 4 terms)
If we take sum as -11. Here n would be 22. At n=22, I would indeed get sum of 1st + 2nd term as -11 itself. Hence, this is the answer.


devashish2407
After the first term in a finite sequence of numbers, each even-numbered term is created by adding 3 to the previous term, and each odd-numbered term is created by multiplying the previous term by –1. How many terms are in the sequence?

(1) The average of all terms in the sequence is \(-\frac{1}{2}\).
(2) The eighteenth term in the sequence is \(–4\).
Show more
Moderators:
Bunuel
Math Expert
113078 posts
FrozenDragon
DI Forum Moderator
409 posts