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In a sequence a1, a2, …, each term after the first is found by taking

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Bunuel
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In a sequence a1, a2, …, each term after the first is found by taking [#permalink] New post   12 Jun 2019, 02:06
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In a sequence \(a_1\),\(a_2\),…, each term after the first is found by taking the negative of the preceding term, and adding 1. If \(a_1 = 2\), what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101
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C
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BrentGMATPrepNow
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Re: In a sequence a1, a2, …, each term after the first is found by taking [#permalink] New post   12 Jun 2019, 05:35
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Bunuel wrote:
In a sequence \(a_1\),\(a_2\),…, each term after the first is found by taking the negative of the preceding term, and adding 1. If \(a_1 = 2\), what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101


Let's list some terms to get a better understanding of the desired sum.
\(a_1 = 2\)
\(a_2 = -2 + 1 = -1\)
\(a_3 = 1 + 1 = 2\)
\(a_4 = -2 + 1 = -1\)
\(a_5 = 1 + 1 = 2\)
\(a_6 = -2 + 1 = -1\)
.
.
.
We can see that all ODD numbered terms are 2, and all EVEN numbered terms are -1

From 1 to 99 inclusive, there are 50 ODD numbered terms and 49 EVEN numbered terms

So, sum = (50)(2) + (49)(-1)
= 100 + (-49)
= 51

Answer: C

Cheers,
Brent
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Re: In a sequence a1, a2, …, each term after the first is found by taking [#permalink] New post   12 Jun 2019, 02:37
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There are 50 odd terms and 49 even terms.

Arvind42 wrote:
Bunuel wrote:
In a sequence \(a_1\),\(a_2\),…, each term after the first is found by taking the negative of the preceding term, and adding 1. If \(a_1 = 2\), what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101


a1=2,a2=-1,a3=2,a4=-1....; So all odd values of n will be 2 and all even values will be -1; 49 Odd terms and 48 even terms; 49*2-48=50 IMO B
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Re: In a sequence a1, a2, …, each term after the first is found by taking [#permalink] New post   17 Jun 2019, 17:48
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Bunuel wrote:
In a sequence \(a_1\),\(a_2\),…, each term after the first is found by taking the negative of the preceding term, and adding 1. If \(a_1 = 2\), what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101


We see that a1 = 2, a2 = -2 + 1 = -1, a3 = 1 + 1 = 2, a4 = -2 + 1 = -1 and so on.

Thus we can see that the odd-numbered terms are all 2 and the even-numbered terms are all -1. Since in the first 99 terms, there are 50 odd-numbered terms and 49 even-numbered terms, then the sum of the first 99 terms is:

50(2) + 49(-1) = 100 - 49 = 51

Answer: C
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In a sequence a1, a2, …, each term after the first is found by taking [#permalink] New post   12 Jun 2019, 02:29
First term=\(a_1\)
Second term = \(-a_1 + 1\)
Third term = \(a_1-1+\)1=\(a_1\)
fourth term = \(-a_1+\)1
And so on

the sum of the first 99 terms= \({49*[a_1+(-a_1+1)]}+a_1\)= 49+2=51

Bunuel wrote:
In a sequence \(a_1\),\(a_2\),…, each term after the first is found by taking the negative of the preceding term, and adding 1. If \(a_1 = 2\), what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101
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In a sequence a1, a2, …, each term after the first is found by taking [#permalink] New post   Updated on: 12 Jun 2019, 21:41
Bunuel wrote:
In a sequence \(a_1\),\(a_2\),…, each term after the first is found by taking the negative of the preceding term, and adding 1. If \(a_1 = 2\), what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101


a1=2,a2=-1,a3=2,a4=-1....; So all odd values of n will be 2 and all even values will be -1; 50 Odd terms and 49 even terms; 50*2-49=51 IMO B

Originally posted by Lampard42 on 12 Jun 2019, 02:35.
Last edited by Lampard42 on 12 Jun 2019, 21:41, edited 1 time in total.
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Re: In a sequence a1, a2, …, each term after the first is found by taking [#permalink] New post   12 Jun 2019, 03:08
Bunuel wrote:
In a sequence \(a_1\),\(a_2\),…, each term after the first is found by taking the negative of the preceding term, and adding 1. If \(a_1 = 2\), what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101


from the given series we can say that odd no are 2 and even are -1
so total odd from 1 to 99 ; 50 and even ; 49
so 50*2+49*(-1) = 51
IMO C
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Re: In a sequence a1, a2, , each term after the first is found by taking [#permalink] New post   04 Mar 2024, 15:47
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Re: In a sequence a1, a2, , each term after the first is found by taking [#permalink]
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