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

Option A:

3

Option B:

4

Option C:

6

Option D:

8

Option E:

9

Option C is the correct answer.

Let there be 3 terms in the sequence, namely a, b & c

Given that a + b + c = 3 * 4 = 12………….. (1)

Now say there are 2 terms, namely a & b

So, a + b = 2 * 3 = 6………. (2)

Substitute value of a+b from eqn (2) in eqn (1)

6 + c = 12

c = 6

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