Sequence - Tricky one

here is how I approached it

Sum upto the 1st term = 1(1+1) = 2 ==> First Term = 2
Sum upto the 2nd term = 2(2+1) = 6 ==> Second Term = 6-2 = 4
Sum upto the 3nd term = 3(3+1) = 12 ==> ThirdTerm = 12-(2+4) = 6

==> OA :C

Hi

Can somebody please explain me to understand this question?
All i know from the above question is ,if we substitute the values 1,2,3 in Sn=n(n+1), we will get 1st term , 2nd term and 3 rd term as 2,6,12,20... respectively.
How is the 3rd term 6???

Thanks

mgm wrote:If Sn is the sum of first n terms of a certain sequence and if Sn = n(n+1) for all positive integers n, which is the third term in the sequence

A)3
b)4
c)6
d)8
E)9

OA: C

The sum of the first term -- in other words, the value of the FIRST TERM ITSELF = 1(1+1) = 2.
The sum of the first 3 terms = 3(3+1) = 12.

We can plug in the answers, which represent the value of the 3rd term.
Since the first term = 2, and the sum of the first 3 terms = 12, the answer choices imply the following sequences:
A: 2, 7, 3
B: 2, 6, 4
C: 2, 4, 6
D: 2, 2, 8
E: 2, 1, 9

Only answer choice C offers a list of terms in ascending order.
Check whether the given formula -- sum = n(n+1) -- accurately calculates the sum of the first 2 terms of answer choice C:
2(2+1) = 2+4
6 = 6.
Success!

The correct answer is C.