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Sequence - Tricky one

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by mgm » Tue Jul 30, 2013 3:53 am
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
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by mgm » Tue Jul 30, 2013 3:59 am
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
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by Brent@GMATPrepNow » Tue Jul 30, 2013 6:31 am
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
Notice that . . .
sum of the first 2 terms = 1st term + 2nd term
sum of the first 3 terms = 1st term + 2nd term + 3rd term

So, 3rd term = (sum of the first 3 terms) - (sum of the first 2 terms)
In other words, 3rd term = S3 - S2
= 3(3+1) - 2(2+1)
= 12 - 6
= 6
= C

Cheers,
Brent
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by kop » Fri Dec 20, 2013 9:32 am
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
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by Brent@GMATPrepNow » Fri Dec 20, 2013 9:44 am
kop wrote: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
In this question, Sn represent the SUM of the first n terms.
So, S1 = (1)(1 + 1) = 2 = the SUM of the first 1 term. In other words, term1 = 2
S2 = (2)(2 + 1) = 6 = the SUM of the first 2 terms. Since term1 = 2, we know that term2 = 4
S3 = (3)(3 + 1) = 12 = the SUM of the first 3 terms. Since term1 = 2, and term2 = 4, we know that term3 = 6

Does that help?

Cheers,
Brent
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by GMATGuruNY » Fri Dec 20, 2013 12:13 pm
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.
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