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Intern  B
Joined: 26 Nov 2017
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The first two terms of a sequence are -3 and 2 Subsequent odd-numbered  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 59% (03:09) correct 41% (02:30) wrong based on 88 sessions

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The first two terms of a sequence are -3 and 2. Subsequent odd-numbered terms are given by adding 1 to the previous term, and subsequent even-numbered terms are given by multiplying the previous term by -1. What is the sum of the first 147 terms?

A. -3
B. -2
C. -1
D. 1
E. 2

Something about this question gives me a hard time. It's a mid 600 level question but I'm struggling to wrap my head around the concept. I get that there's a pattern for this sequence, but struggling on figuring out how to apply that to the 147 terms (i think it's that 1st term at the beginning that's throwing me off).

Originally posted by henrymba2021 on 27 Jan 2018, 10:37.
Last edited by Bunuel on 27 Jan 2018, 10:47, edited 1 time in total.
Renamed the topic and edited the question.
Retired Moderator D
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Posts: 1179
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Re: The first two terms of a sequence are -3 and 2 Subsequent odd-numbered  [#permalink]

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henrymba2021 wrote:
Something about this question gives me a hard time. It's a mid 600 level question but I'm struggling to wrap my head around the concept. I get that there's a pattern for this sequence, but struggling on figuring out how to apply that to the 147 terms (i think it's that 1st term at the beginning that's throwing me off).

Q. The first two terms of a sequence are -3 and 2. Subsequent odd-numbered terms are given by adding 1 to the previous term, and subsequent even-numbered terms are given by multiplying the previous term by -1. What is the sum of the first 147 terms?

a. -3
b. -2
c. -1
d. 1
e. 2

HI henrymba2021

kindly follow the Rules of Posting. Search for the question. there is a high probability, the question would have been discussed in the relevant forum.
Intern  B
Joined: 26 Nov 2017
Posts: 4
Re: The first two terms of a sequence are -3 and 2 Subsequent odd-numbered  [#permalink]

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Hi niks18, I can't find this question in the forum. If you can point me in the right direction that would be much appreciated!
Math Expert V
Joined: 02 Sep 2009
Posts: 58340
Re: The first two terms of a sequence are -3 and 2 Subsequent odd-numbered  [#permalink]

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henrymba2021 wrote:
The first two terms of a sequence are -3 and 2. Subsequent odd-numbered terms are given by adding 1 to the previous term, and subsequent even-numbered terms are given by multiplying the previous term by -1. What is the sum of the first 147 terms?

A. -3
B. -2
C. -1
D. 1
E. 2

Something about this question gives me a hard time. It's a mid 600 level question but I'm struggling to wrap my head around the concept. I get that there's a pattern for this sequence, but struggling on figuring out how to apply that to the 147 terms (i think it's that 1st term at the beginning that's throwing me off).

Please read carefully and follow our RULES OF POSTING. Pay attention to rule 3. Thank you.
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The first two terms of a sequence are -3 and 2 Subsequent odd-numbered  [#permalink]

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1
Hey henrymba2021

It has been given that the first and second terms of the sequence are -3 and 2

Third term(odd term) can be got by adding 1 to the previous term, which is 2+1 = 3
Fourth term(even) can be got by multiplying -1 to the previous term, which is -3

Fifth term = -2, Sixth term = 2, Seventh term is 3, Eight term is -3

If you observe there is a pattern where the odd and even terms cancel each other.
The 147th term will be 3.

The sum of the 147 terms will be -3 + 2 + 0 + 0 + .... + 3 = 2(Option E)
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Manager  B
Joined: 23 Oct 2017
Posts: 61
Re: Arithmetic Question - 600 Level - Need Explanation  [#permalink]

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1
Given: The first two terms of a sequence are -3 and 2. Subsequent odd-numbered terms are given by adding 1 to the previous term, and subsequent even-numbered terms are given by multiplying the previous term by -1

Try constructing the series by following the problem stmt:
Inital terms: -3 & 2

1st term: 2+1=3,
2nd term: 3*(-1)=-3,
3rd term: -3+1=-2,
4th term: -2*(-1)=2,
5th term: 2+1=3
6th term: 3*(-1) =-3

For now, lets remove -3 & 2 the intial terms out of the sequence
By now you will notice that it follows a unique sequence: 3,-3,2,-2,3,-3 ....

odd + even terms =0
Since there are 147 -2 =145 terms there will be one term which is left out = 3

As every 4n+1 th term =3 (4n+2 th term =-3, 4n+3 th term =2, 4n+4 th term=-2)

Bring back the intial terms -3 & 2.
Thus, sum = -3 + 2 +3 =2
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Re: The first two terms of a sequence are -3 and 2 Subsequent odd-numbered  [#permalink]

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pushpitkc wrote:
Hey henrymba2021

It has been given that the first and second terms of the sequence are -3 and 2

Third term(odd term) can be got by adding 1 to the previous term, which is 2+1 = 3
Fourth term(even) can be got by multiplying -1 to the previous term, which is -3

Fifth term = -2, Sixth term = 2, Seventh term is 3, Eight term is -3

If you observe there is a pattern where the odd and even terms cancel each other.
The 147th term will be 3.

The sum of the 147 terms will be -3 + 2 + 0 + 0 + .... + 3 = 2(Option E)

Hi pushpitkc. hope you are having fantastic GMAT weekend with GMATclub now back to question:-)

why the first two letters and the last 3 didnt cancel out if other numbers canceled out ? -3 + 2 + 0 + 0 + .... + 3

thanks! Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3344
Location: India
GPA: 3.12
The first two terms of a sequence are -3 and 2 Subsequent odd-numbered  [#permalink]

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Hi dave13

First term is -3
Second term is 2
Third(3) and fourth term(-3) cancel each other out.
Seventh(-2) and eighth term(2) cancel each other out.
Ninth(3) and tenth term(-3) cancel each other out.
.
.
We observe a pattern in the terms from 3rd term(3 -3 -2 2 3 -3 -2 2 3 -3 -2 2.....)
.
.
145th term(-2) and 146th term(2) cancel each other out.
147th term will be 3.

So sum is -3 + 2 + 3+ (-3) + (-2) + 2 ......... + (-2) + 2 + 3 = -3 + 2 + 3 = 2

P.S The alternate terms starting from the 3rd term till the 146th term cancel each other out

Hope this helps clear your confusion.
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You've got what it takes, but it will take everything you've got The first two terms of a sequence are -3 and 2 Subsequent odd-numbered   [#permalink] 27 Jan 2018, 12:58
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