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# The sequence A is defined by the following relationship:

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Math Expert
Joined: 02 Sep 2009
Posts: 60473
The sequence A is defined by the following relationship:  [#permalink]

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07 Nov 2019, 02:13
00:00

Difficulty:

65% (hard)

Question Stats:

62% (02:34) correct 38% (03:02) wrong based on 61 sessions

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The sequence A is defined by the following relationship: $$A_n=A_{n-1}+(-1)^{n+1}(n)^2$$ for all integer values $$n >1$$. If $$A_1=1$$ , what is $$A_{15}-A_{13}$$ ?

A. 14
B. 29
C. 169
D. 196
E. 421

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Location: India
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Re: The sequence A is defined by the following relationship:  [#permalink]

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07 Nov 2019, 10:38
for the given function $$A_n=A_{n-1}+(-1)^{n+1}(n)^2$$
A1=1
A2=-3
A3= 6
A4=-10
A5=15
A6=-21
.
.
.
.
A13= 91 and A15= 120
A15-A13 = 29
IMO B

if there is any other short cut please share..

Bunuel wrote:
The sequence A is defined by the following relationship: $$A_n=A_{n-1}+(-1)^{n+1}(n)^2$$ for all integer values $$n >1$$. If $$A_1=1$$ , what is $$A_{15}-A_{13}$$ ?

A. 14
B. 29
C. 169
D. 196
E. 421

Are You Up For the Challenge: 700 Level Questions
Intern
Joined: 12 Oct 2019
Posts: 41
Location: India
Concentration: Marketing, General Management
GMAT 1: 720 Q48 V41
GPA: 4
WE: Information Technology (Computer Software)
Re: The sequence A is defined by the following relationship:  [#permalink]

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08 Nov 2019, 05:55
A1=1
A2=-3
A3=6
A4=-10

Once we have found out till A4 we can see the pattern for the next term: add n to the absolute value of the previous and reverse the sign. For e.g. A5 = |A4| + 5 (with reversed sign).
So we can then quickly find out:

A5=15
A6=-21
A7=28
A8=-36
.
.
.
A13=91
A14=-105
A15=120

Hence A15-A13 = 29

B
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Joined: 10 Mar 2018
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GPA: 3.85
The sequence A is defined by the following relationship:  [#permalink]

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18 Dec 2019, 00:24
4
You should start from the ending, using the sequence formula.

A15 - A13 = A14 + 15^2 - A13 = A13 - 14^2 + 15^2 - A13 = (15-14) * (15+14) = 29
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Joined: 06 Feb 2019
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Re: The sequence A is defined by the following relationship:  [#permalink]

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20 Dec 2019, 07:35
Har8 wrote:
You should start from the ending, using the sequence formula.

A15 - A13 = A14 + 15^2 - A13 = A13 - 14^2 + 15^2 - A13 = (15-14) * (15+14) = 29

Very elegant solution!
Thank you.

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Joined: 27 Nov 2016
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Concentration: Finance, Entrepreneurship
Re: The sequence A is defined by the following relationship:  [#permalink]

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20 Dec 2019, 08:36
A1 = 1
A2 = -3
A3 = 6
A4= -10
A5=15
once we figure out a pattern it will simple and we Even Dont need to find out what A15 , A14 AND A13 is.

Difference between each term is mod n or |N| i.e. ||A2|-|A1|| =2 , ||A3|-|A2|| = 3, ||A4|-|A3|| =4
A15-A13=||A15|-|A14||+||A14|-|A13|| === 15+14 =29

So Answer is B, and we even didnt need to calculate all the numbers
Re: The sequence A is defined by the following relationship:   [#permalink] 20 Dec 2019, 08:36
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