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Sequences

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Sequences

by evansbd » Fri Jul 18, 2008 10:26 am
I gathered a bunch of questions, then forgot where these originated from. I believe it was an old thread from this group but I can't find the threads.


1)In a sequence, each term is obtained by adding 4 to the preceding one. If the sum of the first 10 terms is equal to 80, what is the result of the addition of the first 40 terms?





2)In a group of 10 girls, only 4 girls have blue eyes. If 3 girls are to be selected at random, without replacement, what is the probability that at least 2 girls will have blue eyes?




Any solutions? Or just the links to the earlier discussions....
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by seweryn » Fri Jul 18, 2008 10:59 am
just write it out x+(x+4)+(x+8 )...+(x+36)=80
solve 10x+180=80, x=-10
for 40 times, 40(-10)+720=320.

or knowing that sum of 10 items is 80, multiply by 4 to solve for 40th term, 80*4=320
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Comination...

by evansbd » Fri Jul 18, 2008 11:08 am
I think....

the answer to the second question is (4C2)/(10C3) = 1/6
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Re: Comination...

by parallel_chase » Fri Jul 18, 2008 12:26 pm
evansbd wrote:I think....

The answer to the second question is (4C2)/(10C3) = 1/6
Well the question says at least 2 girls, means more than 2 will also be taken into account.

4C2 * 6C1 / 10C3

+

4C3*6C0 / 10C3

= 1/3


Let me if you think otherwise.
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Comination...

by evansbd » Fri Jul 18, 2008 12:54 pm
Definitely...I never accounted for all 3 girls being chosen
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by parallel_chase » Fri Jul 18, 2008 1:28 pm
seweryn wrote:just write it out x+(x+4)+(x+8 )...+(x+36)=80
solve 10x+180=80, x=-10
for 40 times, 40(-10)+720=320.

or knowing that sum of 10 items is 80, multiply by 4 to solve for 40th term, 80*4=320
Sum of n terms = n/2[2a+(n-1)d]

x+(x+4)+(x+8 )...+(x+36)=80

Sum of first 10 terms

10/2[2x+(10-1)4] = 80

x = -10

Sum of first 40 terms

40/2[2(-10) + (40-1)4] => 2720

Let me know what you think.
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by asigheartau » Fri Jul 18, 2008 8:36 pm
Question 1:
Agreed with parallel_ chase

Sum of the first ten (i.e. x, x+ 4,X+8, ... X+36) or ( X+1x4,X+ 2x4,3x4....X+9x4)

Knowing that the sum of the first 10 numbers is 80
x= -10

Now for the first 40 numbers: In order to make it easier, let us isolate the x's and the multiples of 4

Hence,

eq. 1:40 x= -400

eq.2 (1X4+ 2X4+...... +39X4) equals to [(39X4)X40]/2 = 3120

3120-400= 2720

Of course you don`t have to go through all this presentation but there is a formula to be used in any sequence:

this formula specifies that for a number of n elements in a sequence, the sum of the elements is [n(n+1)]/2

To illustrate:

{1+2+3+4}= 10

Using the formula, the sum would be : [4(5)]/2= 10

Q.2

Since we are asked for AT LEAST two girls with blue eyes, the third spot can be taken by any of the rest of the girls.

Therefore, we add the combinations above mentioned to get the result of 1/3.
Alin Sigheartau
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