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# What is the sum of the series 12, 2, 15, -1, 18, -4, 21, -7, ..... 30?

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What is the sum of the series 12, 2, 15, -1, 18, -4, 21, -7, ..... 30? [#permalink]
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lnm87 wrote:
What is the sum of the series 12, 2, 15, -1, 18, -4, 21, -7, ..... 30?

A. 74
B. 84
C. 94
D. 104
E. 114

Since, we are given almost 8 to 9 numbers in a sequence, we can easily find the sequence..
There are two series - one odd numbered and one even numbered
a, b, a+3, b-3, a+6, b-6, .......a+3n
when you add any pair starting from left the sum is a+b, a+3+b-3=a+b..

So how many pairs are there..
12,_, 15,_...,24,x,27,x+3,30

So number of pairs are till 27+x+3....=$$\frac{27-12}{3}+1=6$$
Sum = $$(12+2)*6+30=14*6+30=84+30=114$$

E
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Re: What is the sum of the series 12, 2, 15, -1, 18, -4, 21, -7, ..... 30? [#permalink]
GMATPrepNow wrote:
It's important to note that the GMAT won't test our ability to find missing terms in a sequence unless the sequence is defined for us.
The reason is that there's no way that we can definitively determine ONE (and ONLY ONE) pattern in a given sequence.

Consider this example: 1, 2, 4, __
What's the missing term here?
Well, if we read the sequence as doubling from one term to the next, the next term is 8
HOWEVER, if we notice that we keep adding successively larger integers to each term (i.e., add 1, then add 2, then add 3, etc.) the next term is 7

Likewise, (if we want to get a bit silly), we might look at the given sequence (5, 28, 57, 78, 125, __) and say that the missing term is 88. Why?
Because 5 is my favorite number, 28 is my 2nd favorite number, 57 is my 3rd favorite number, ... and 88 is 6th favorite number.

So, rest assured, you won't be required to find missing terms on a GMAT sequence, unless the sequence is defined for us.

Cheers,
Brent

For the first time, I figured out that fourth term is sum of first two terms minus third and that goes till the element is 30(later found n = 13). However, i ran out of patience and left it estimating D as answer.
So, my question is.. would a question appear if it's got a solution?
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Re: What is the sum of the series 12, 2, 15, -1, 18, -4, 21, -7, ..... 30? [#permalink]
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12+2, 15-1, 18-4,.....,30
14, 14, 14...,30
14*6+30= 114

E is answer.
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Re: What is the sum of the series 12, 2, 15, -1, 18, -4, 21, -7, ..... 30? [#permalink]
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What is the sum of the series 12, 2, 15, -1, 18, -4, 21, -7, ..... 30?

A. 74
B. 84
C. 94
D. 104
E. 114-->correct

Solution-1:
12+2 + 15 + (-1) + 18+ (-4) + 21+(-7) + ..... +30
= 14 + 14 + +14 +. +14+30
= 14*6+30 -->30=12+(n-1)*3, so 30 is the 7th term, so there are 6 14s before 30
= 84+30
=114

Solution-2:
12, 2, 15, -1, 18, -4, 21, -7, ..... 30
two series:
1st: 12, 15, 18, ....., 30 --> 30=12+(n-1)*3,so 30 is the 7th term
2nd: 2,-1,-4,-7,.... --> from 1st series, we can saym 2nd series has n-1=6 terms
so 2nd: 2,-1,-4,-7,.... -13 --> because 6th term = 2+(6-1)*(-3)=-13
sum of 1st series(7terms): 7*(12+30)/2=7*21=147
sum of 2nd series(6terms): 6*(2-13)/2=3*(-11)=-33
so sum of 1st + 2nd series = 114
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Re: What is the sum of the series 12, 2, 15, -1, 18, -4, 21, -7, ..... 30? [#permalink]
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lnm87 wrote:
What is the sum of the series 12, 2, 15, -1, 18, -4, 21, -7, ..... 30?

A. 74
B. 84
C. 94
D. 104
E. 114

Series = 12,2,15,-1,18,-4,21,-7,24,-10,27,-13,30
12+2 = 15-1 = 18-4 = 21 -7 = 24-10 = 27-13 = 14
Sum = 14*6+30 = 114

IMO E
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Re: What is the sum of the series 12, 2, 15, -1, 18, -4, 21, -7, ..... 30? [#permalink]
Expert Reply
Top Contributor
unraveled wrote:
GMATPrepNow wrote:
It's important to note that the GMAT won't test our ability to find missing terms in a sequence unless the sequence is defined for us.
The reason is that there's no way that we can definitively determine ONE (and ONLY ONE) pattern in a given sequence.

Consider this example: 1, 2, 4, __
What's the missing term here?
Well, if we read the sequence as doubling from one term to the next, the next term is 8
HOWEVER, if we notice that we keep adding successively larger integers to each term (i.e., add 1, then add 2, then add 3, etc.) the next term is 7

Likewise, (if we want to get a bit silly), we might look at the given sequence (5, 28, 57, 78, 125, __) and say that the missing term is 88. Why?
Because 5 is my favorite number, 28 is my 2nd favorite number, 57 is my 3rd favorite number, ... and 88 is 6th favorite number.

So, rest assured, you won't be required to find missing terms on a GMAT sequence, unless the sequence is defined for us.

Cheers,
Brent

For the first time, I figured out that fourth term is sum of first two terms minus third and that goes till the element is 30(later found n = 13). However, i ran out of patience and left it estimating D as answer.
So, my question is.. would a question appear if it's got a solution?

The GMAT will not give you a sequence (or series) in which the terms aren't specifically defined (for the reasons I mentioned above).
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Re: What is the sum of the series 12, 2, 15, -1, 18, -4, 21, -7, ..... 30? [#permalink]
How are there 6 terms in the second series?

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Re: What is the sum of the series 12, 2, 15, -1, 18, -4, 21, -7, ..... 30? [#permalink]
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Re: What is the sum of the series 12, 2, 15, -1, 18, -4, 21, -7, ..... 30? [#permalink]
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