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Some good questions..Require solution [#permalink]

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08 Nov 2009, 11:18

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1. A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?

A. 5 B. 6 C. 7 D. 8 E. 9

2.The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4. What is the sum of the first 97 terms of the sequence?

Re: Some good questions..Require solution [#permalink]

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08 Nov 2009, 11:51

alok2171 wrote:

1. A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?

A. 5 B. 6 C. 7 D. 8 E. 9

8 ways

Assuming 1 office # of ways with 3 employees = 1 # of ways with 2 employees = 3 total = 4 two office so answer = 8

Re: Some good questions..Require solution [#permalink]

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08 Nov 2009, 12:02

alok2171 wrote:

2.The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4. What is the sum of the first 97 terms of the sequence?

A. 72 B. 74 C. 75 D. 78 E. 80

a1 = 2 a2 = -3 a3 = 5 a4 = -1 a5=a5-4= a1 a6=a2 and so on and so forth

In other words, the 4 numbers given are the only ones in the sequence We need 97 terms total. Therefore, each term will be seen at least 24 times and 4 times 24 = 96 and the first number will be seen 5 times because we need 97 total:

2 x 25 = 50 -3 x 24 = -72 5 x 24 = 120 -1 x 24 = -24

1. A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?

A. 5 B. 6 C. 7 D. 8 E. 9

Each of 3 employees has 2 offices to be assigned so the total # of ways is 2^3=8

Answer: D

alok2171 wrote:

2.The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4. What is the sum of the first 97 terms of the sequence?

A. 72 B. 74 C. 75 D. 78 E. 80

I guess that an=an-4? If so than:

a1=a5, a2=6, a3=a7 etc. So we'll have the sequence 2,-3,5,-1, 2,-3,5,-1, 2,-3,5,-1, ... 97 terms.

The sum of group of four terms 2,-3,5,-1 is 3. We'll have 97/4=24 full groups of four, plus 97th term 2.

The infinite sequence a1, a2,..., an,... is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4. What is the sum of the first 97 terms of the sequence? A. 72 B. 74 C. 75 D. 78 E. 80

The infinite sequence a1, a2,..., an,... is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4. What is the sum of the first 97 terms of the sequence? A. 72 B. 74 C. 75 D. 78 E. 80

Is An = A (n-4) ?

If yes then the answer should be B

A5= A (5-4) = A 1 = 2 similarly A 6 = -3 and this sequence will repeat after every 4 terms

A1 + A 2+ A3 + A4 = 2- 3+ 5-1 = 3

now Sum of first 96 terms = 3 *24 Sum of 97 terms = 72 + 2 = 74

Last edited by cipher on 02 May 2010, 10:54, edited 1 time in total.

The infinite sequence a1, a2,..., an,... is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4. What is the sum of the first 97 terms of the sequence? A. 72 B. 74 C. 75 D. 78 E. 80

Is An = A (n-4) ?

If yes then the answer should be B

A5= A (5-4) = A 1 = 2 similarly A 6 = -3 and this sequence will repeat after every 4 terms

A1 + A 2+ A3 + A4 = 2- 3+ 5-1 = 2

now Sum of first 96 terms = 2 *24 Sum of 97 terms = 72 + 2 = 74

I understood until the point that as after 4 we have repeat of the sequence, you can say 96/4= 24...as sum of 4 terms is 2, so 2*24= 48...from where did 72 come from...can you explain it further....

The infinite sequence a1, a2,..., an,... is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4. What is the sum of the first 97 terms of the sequence? A. 72 B. 74 C. 75 D. 78 E. 80

Is An = A (n-4) ?

If yes then the answer should be B

A5= A (5-4) = A 1 = 2 similarly A 6 = -3 and this sequence will repeat after every 4 terms

A1 + A 2+ A3 + A4 = 2- 3+ 5-1 = 2

now Sum of first 96 terms = 2 *24 Sum of 97 terms = 72 + 2 = 74

I understood until the point that as after 4 we have repeat of the sequence, you can say 96/4= 24...as sum of 4 terms is 2, so 2*24= 48...from where did 72 come from...can you explain it further....

my bad again the was 3 and not 3 edited the post ..!