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# In a sequence for which an=a(n−1)+(−1)n(n)(k) for all values n>1 , wh

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Joined: 08 Apr 2017
Posts: 78
In a sequence for which an=a(n−1)+(−1)n(n)(k) for all values n>1 , wh  [#permalink]

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21 Apr 2018, 04:36
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65% (hard)

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61% (02:41) correct 39% (03:10) wrong based on 50 sessions

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In a sequence for which $$a_{n}$$=$$a_{(n−1)}$$+$$(−1)^{n}$$(n)(k) for all values n>1, where k is a constant and $$a_{1}$$=k, what is the value of $$a_{100}$$?

A. 53k

B. 52k

C. 48k

D. 47k

E. 23k
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Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82
Re: In a sequence for which an=a(n−1)+(−1)n(n)(k) for all values n>1 , wh  [#permalink]

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21 Apr 2018, 06:09
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sachinpoovanna wrote:
In a sequence for which $$a_{n}$$=$$a_{(n−1)}$$+$$(−1)^{n}$$(n)(k) for all values n>1, where k is a constant and $$a_{1}$$=k, what is the value of $$a_{100}$$?

A. 53k

B. 52k

C. 48k

D. 47k

E. 23k

$$a_{n}=a_{(n−1)}+(−1)^{n}(n)(k)$$

$$a_{2}=a_{1}+(−1)^{2}(2)(k)=k+2k=3k$$

$$a_{3}=a_{2)}+(−1)^{3}(3)(k)=0$$

$$a_{4}=a_{3)}+(−1)^{4}(4)(k)=4k$$

So we have our series as k,3k,0,4k.....

In this series even terms of the series are, 3k, 4k,.......$$a_{100}$$

$$a_{100}$$, will be the 50th term of this even series and can be found out by using the AP formula -

$$t_n=a+(n-1)*d=>a_{100}=3k+(50-1)*k=52k$$

Option $$B$$
Math Expert
Joined: 02 Aug 2009
Posts: 7199
Re: In a sequence for which an=a(n−1)+(−1)n(n)(k) for all values n>1 , wh  [#permalink]

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21 Apr 2018, 06:11
sachinpoovanna wrote:
In a sequence for which $$a_{n}$$=$$a_{(n−1)}$$+$$(−1)^{n}$$(n)(k) for all values n>1, where k is a constant and $$a_{1}$$=k, what is the value of $$a_{100}$$?

A. 53k

B. 52k

C. 48k

D. 47k

E. 23k

look at the series..
$$a_2=k+k=2k........a_3=2k-3k=-k........a_4=-k+4k=3k.....a_5=3k-5k=-2k.......a_6=-2k+6k=4k$$ and so on..
so even numbers, say a_x, is $$a_x=xk-\frac{(x-4)k}{2}$$..
thus $$a_{100}=100k-\frac{(100-4)k}{2}=100k-48k=52k$$

B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: In a sequence for which an=a(n−1)+(−1)n(n)(k) for all values n>1 , wh &nbs [#permalink] 21 Apr 2018, 06:11
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