Sn is the sum of the first n terms

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 am; Location: Jeddah, Saudi Arabia; Thanked: 42 times; Followed by:7 members; GMAT Score:730

Sn is the sum of the first n terms

by faraz_jeddah » Wed Sep 11, 2013 9:32 am

If Sn is the sum of the first n terms of a certain sequence and if Sn = n(n+1) for all positive intergers n, what is the 3rd term of the sequence

A - 3
B - 4
c - 6
D - 8
E - 9

I have encountered this problem 3 times and I still end up picking the wrong answer.

I get confused in my approach
One statement tells me
S1 = 2 ; S2 = 6 ; S3 = 12
The other statement tells
S3 = 2 + 6 = 8

I always end up choosing 8, which is wrong.

A good question also deserves a Thanks.

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adthedaddy: Master | Next Rank: 500 Posts; Posts: 167; Joined: Fri Mar 09, 2012 8:35 pm; Thanked: 39 times; Followed by:3 members

by adthedaddy » Wed Sep 11, 2013 9:47 am

Hi Faraz, you can solve this problem this way -

For the given condition, Sn=n(n+1) where n=positive integers

We start substituting with n=1 -

S1 = 1(1+1) = 2
S2 = 6
S3 = 12

Now, for n=1, Sn=2, thus sequence starts with number 2.
Then, sum of first two nos is S2 which is 6. Thus, first two nos are 2,4
Next, sum of first three nos is S3=12 i.e. first 3 numbers are 2,4,6

From the above sequence, the 3rd number is 6 (Option C)

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sanjoy18: Senior | Next Rank: 100 Posts; Posts: 81; Joined: Tue Jun 11, 2013 10:24 pm; Thanked: 7 times; Followed by:1 members

by sanjoy18 » Wed Sep 11, 2013 10:02 am

use this formula when sn is given

Tn=nth term of term of the series

Tn=Sn -S(n-1)

and T1=S1

T1=2
T2=s2-s1=6-2=4

T3=s3-s2=12-6=6

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Java_85: Master | Next Rank: 500 Posts; Posts: 234; Joined: Tue Jul 16, 2013 9:00 am; Location: West Virginia; Thanked: 9 times

by Java_85 » Wed Sep 11, 2013 10:05 am

Good question, C it is.

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 am; Location: Jeddah, Saudi Arabia; Thanked: 42 times; Followed by:7 members; GMAT Score:730

by faraz_jeddah » Wed Sep 11, 2013 10:09 am

adthedaddy wrote:Hi Faraz, you can solve this problem this way -

For the given condition, Sn=n(n+1) where n=positive integers

We start substituting with n=1 -

S1 = 1(1+1) = 2
S2 = 6
S3 = 12

Now, for n=1, Sn=2, thus sequence starts with number 2.
Then, sum of first two nos is S2 which is 6. Thus, first two nos are 2,4
Next, sum of first three nos is S3=12 i.e. first 3 numbers are 2,4,6

From the above sequence, the 3rd number is 6 (Option C)

Thanks Amigo! Makes sense now.

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ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pm; Location: Bangalore, India; Thanked: 97 times; Followed by:26 members; GMAT Score:750

by ganeshrkamath » Wed Sep 11, 2013 11:55 pm

faraz_jeddah wrote:If Sn is the sum of the first n terms of a certain sequence and if Sn = n(n+1) for all positive intergers n, what is the 3rd term of the sequence

A - 3
B - 4
c - 6
D - 8
E - 9

I have encountered this problem 3 times and I still end up picking the wrong answer.

I get confused in my approach
One statement tells me
S1 = 2 ; S2 = 6 ; S3 = 12
The other statement tells
S3 = 2 + 6 = 8

I always end up choosing 8, which is wrong.

S1 = 1(1+1) = 2
T1 = 2

S2 = 2(2+1) = 6
T2 = S2 - S1 = 4

S3 = 3(3+1) = 12
T3 = S3 - S2 = 6

Choose C

I think you have taken both sum of n terms and the nth term as the same.

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by Scott@TargetTestPrep » Tue Jan 09, 2018 9:49 am

faraz_jeddah wrote:If Sn is the sum of the first n terms of a certain sequence and if Sn = n(n+1) for all positive intergers n, what is the 3rd term of the sequence

A. 3
B . 4
c . 6
D . 8
E . 9

We see that S3 = 3(4) = 12 and S2 = 2(3) = 6. Since S3 is the sum of the first three terms and S2 is the sum of the first two terms, the difference, S3 - S2 = 12 - 6 = 6, must be the value of the third term of the sequence.

Answer: C

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