GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 25 Jan 2020, 03:20

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 08 Apr 2017
Posts: 72
In a sequence for which an=a(n−1)+(−1)n(n)(k) for all values n>1 , wh  [#permalink]

### Show Tags

21 Apr 2018, 05:36
6
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:49) correct 36% (02:51) wrong based on 67 sessions

### HideShow timer Statistics

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
Retired Moderator
Joined: 25 Feb 2013
Posts: 1156
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]

### Show Tags

21 Apr 2018, 07:09
1
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: 8336
Re: In a sequence for which an=a(n−1)+(−1)n(n)(k) for all values n>1 , wh  [#permalink]

### Show Tags

21 Apr 2018, 07:11
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
_________________
Manager
Joined: 04 Oct 2018
Posts: 158
Location: Viet Nam
Re: In a sequence for which an=a(n−1)+(−1)n(n)(k) for all values n>1 , wh  [#permalink]

### Show Tags

05 Apr 2019, 09:50
GMATSkilled 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

a2 = 3k,
a4 = 4k = a2 + k
a6 = 5k = a2 + 2k
a8 = 6k = a2 + 3k
...
a(n) = a2 + (n-2)/2 *k => a100 = 3k + (100 - 2)/2 * k = 3k + 49k = 52k. Hence B
_________________
"It Always Seems Impossible Until It Is Done"
Re: In a sequence for which an=a(n−1)+(−1)n(n)(k) for all values n>1 , wh   [#permalink] 05 Apr 2019, 09:50
Display posts from previous: Sort by