Sn is the sum of the first n terms

[faraz_jeddah]

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.

[adthedaddy]

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)

[sanjoy18]

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

[Java_85]

Good question, C it is.

[faraz_jeddah]

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.

[ganeshrkamath]

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.

Cheers

[Scott@TargetTestPrep]

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