Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 2807:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 28, 2026 - Oct. 16, 2027, 7:00pm-10:00pm EST
Sep 2911:00 AM EDT
-01:00 PM EDT
" Description: Top scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thur Sept. 29, 2026 - Dec. 3, 2026, 11:00am-1:00pm EST
Oct 0107:00 AM BST
-08:00 AM GMT
Welcome to the GMAT Club's Free Interview Prep Event for Top MBA Programs! Buy tickets - Virtual series that’s all set to equip you to -excel in your MBA interviews.
Oct 0301:00 PM EDT
-04:00 PM EDT
Top scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Saturdays Oct. 3, 2026 - Dec. 26, 2026, 1:00pm-4:00pm EST
26 Dec 2023, 06:33
Kudos
Bookmarks
\(a_{1}\): 4
\(d\): 6
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (01:58) correct
42%
(02:00)
wrong
based on 1353
sessions
History
Date
Time
Result
Not Attempted Yet
In an arithmetic sequence, the sum, \(S_{n}\) of the first \(n\) terms of the sequence equals \(n + 3n^2\) for all \(n\).
In the table, select a value for the first term, \(a_{1}\), of the sequence, and a value for the difference, \(d\), between successive terms of the sequence.
In the table, select a value for the first term, \(a_{1}\), of the sequence, and a value for the difference, \(d\), between successive terms of the sequence.
| \(a_{1}\) | \(d\) | |
| 2 | ||
| 4 | ||
| 6 | ||
| 8 | ||
| 10 | ||
| 12 |
ShowHide Answer
Official Answer
\(a_{1}\): 4
\(d\): 6
26 Dec 2023, 06:57
Kudos
Bookmarks
Sajjad1994
\(S_n\) is the sum of the first n terms.
Substitute n=1: \(S_1=n + 3n^2=1+3*1^2=4\), but \(S_1\) is nothing but the first term. So, \(a_1=4\)
Substitute n=2: \(S_2=n + 3n^2=2+3*2^2=14\), but \(S_2\) is nothing but the sum of first two terms => \(S_2=a_1+a_2......14=4+a_2.......a_2=10\). So, \(d=a_2-a_1=10-4=6\)
General Discussion
24 Aug 2024, 23:41
Kudos
Bookmarks
Sn is the sum of the first n terms.
Given, sequence is an Arithmentic Sequence. And sum of first n terms of that sequence is: \(n + 3n^2\) ---> Eq 1
Formula for for sum of first n terms of an Arithmetic Sequence is: \( Sn= n/2* [ 2a + ( n − 1 )d ]\). ----> Eq 2
Equate 1 and 2.
\( n + 3n^2 = n /2* [ 2a + ( n − 1 )d ]\)
Expand the above -
\(2n + 6n^2= (2a-d)n + d(n^2)\)
Compare n^2 terms on LHS and RHS -
\( 6n^2 = d(n^2) \)
d=6
Compare n terms on LHS and RHS -
\((2a-d)n=2n\)
\(2a-d=2\)
Substituting d=6;
\(2a=8\)
a=4
Given, sequence is an Arithmentic Sequence. And sum of first n terms of that sequence is: \(n + 3n^2\) ---> Eq 1
Formula for for sum of first n terms of an Arithmetic Sequence is: \( Sn= n/2* [ 2a + ( n − 1 )d ]\). ----> Eq 2
Equate 1 and 2.
\( n + 3n^2 = n /2* [ 2a + ( n − 1 )d ]\)
Expand the above -
\(2n + 6n^2= (2a-d)n + d(n^2)\)
Compare n^2 terms on LHS and RHS -
\( 6n^2 = d(n^2) \)
d=6
Compare n terms on LHS and RHS -
\((2a-d)n=2n\)
\(2a-d=2\)
Substituting d=6;
\(2a=8\)
a=4
