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# The sequence A is defined by the following relationship:

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Intern
Joined: 08 Sep 2016
Posts: 35
Location: Georgia
GPA: 3.75
WE: Analyst (Investment Banking)
The sequence A is defined by the following relationship:  [#permalink]

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23 Mar 2017, 09:18
5
4
00:00

Difficulty:

65% (hard)

Question Stats:

65% (03:09) correct 35% (02:49) wrong based on 119 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

Hit kudos if you liked the question
Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: The sequence A is defined by the following relationship:  [#permalink]

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23 Mar 2017, 09:59
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4
giobas 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

Hit kudos if you liked the question

Hi

$$A_n - A_{n-1} =$$ $$(-1)^{n+1}$$$$(n)^2$$

$$A_{15} - A_{14} = (-1)^{16} * 225 = 225$$

$$A_{14} - A_{13} = (-1)^{15}*196 = -196$$

$$A_{15} - A_{14} + A_{14} - A_{13} = A_{15} - A_{13} = 225 - 196 = 29$$

##### General Discussion
Manager
Joined: 08 Sep 2016
Posts: 115
The sequence A is defined by the following relationship:  [#permalink]

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03 Apr 2018, 14:19
1
Brutal problem but I was able to see the pattern after over 2 minutes of trying it out.

A1 = 1
A2 = -3
A3 = 6
A4 = -10
A5 = 15

There's a pattern here. The odd sequence number multiplied by the progression step equal value (i'm not sure if that makes sense haha).

Example:
A1 = 1*1= 1
A3 = 3*2 = 6
A5 = 5*3= 15
....
A13 = 13*7 = 91
A15 = 15*8 = 120

A15 - A13 = 120-91 = 29.

The sequence A is defined by the following relationship: &nbs [#permalink] 03 Apr 2018, 14:19
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