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Arithmetic Progression

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Current Student
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Arithmetic Progression  [#permalink]

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New post 12 Aug 2016, 07:54
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Hi Everyone

I Find that there are several questions on the gmat regarding the Combination of Statistics and Arithmetic Progression.

Just created some bullet Points
If i am missing anything or anyone of these statements is untrue please notify me here




A)AP is a series in which each term after the first term is just a constant being added to its immediate preceding term => a,a+d,a+2d.....,a+(n-1)d

B) a(n)= a+(n-1)d i.e the nth term of any AP e.g=> 23rd term = a+22d

C) s(n) = n/2[2a+(n-1)d]

D)s(n) = n/2[a+l]

E) In an AP Mean = Median = 1/2[sum of last and first term] = 1/2[sum of second and second last term ] and so on.

Here mean = median [as the sum of deviations around the mean is zero]

E.g.
Mean of integers from 45,46,46...100 => (100+45)/2 =72.5
Mean of integers from 200,201,202....300 => (200+300)/2 =250
Additionally
If a,b,c,d,e,f,g, are in AP
Mean = Median = d
Now removing the elements in combination such as a and g or b and f or a,b,f,g doesn't effect the mean or the median
This can easily be understood using the definition of mean => Mean of any dataset is a value for which the sum of deviations around it is zero
After Removing these terms mentioned above the mean does not get effected as still for each and every and every -ve deviation around the mean there is an equal and opposite +ve deviation of same magnitude.

F) Consecutive evens , Consecutive odds , consecutive integers are all AP series


G) Sum of any N consecutive integers is always divisible by N for N being ODD (Not for even)

So the average of N consecutive integers is an integer for N being ODD

H) Product of n consecutive integers is always is always divisible by n!

Anything else ?


Regards
Stone Cold
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Arithmetic Progression  [#permalink]

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New post 24 Aug 2016, 02:07
1
stonecold wrote:
Hi Everyone

I Find that there are several questions on the gmat regarding the Combination of Statistics and Arithmetic Progression.

Just created some bullet Points
If i am missing anything or anyone of these statements is untrue please notify me here




A)AP is a series in which each term after the first term is just a constant being added to its immediate preceding term => a,a+d,a+2d.....,a+(n-1)d

B) a(n)= a+(n-1)d i.e the nth term of any AP e.g=> 23rd term = a+22d

C) s(n) = n/2[2a+(n-1)d]

D)s(n) = n/2[a+l]

E) In an AP Mean = Median = 1/2[sum of last and first term] = 1/2[sum of second and second last term ] and so on.

Here mean = median [as the sum of deviations around the mean is zero]

E.g.
Mean of integers from 45,46,46...100 => (100+45)/2 =72.5
Mean of integers from 200,201,202....300 => (200+300)/2 =250
Additionally
If a,b,c,d,e,f,g, are in AP
Mean = Median = d
Now removing the elements in combination such as a and g or b and f or a,b,f,g doesn't effect the mean or the median
This can easily be understood using the definition of mean => Mean of any dataset is a value for which the sum of deviations around it is zero
After Removing these terms mentioned above the mean does not get effected as still for each and every and every -ve deviation around the mean there is an equal and opposite +ve deviation of same magnitude.

F) Consecutive evens , Consecutive odds , consecutive integers are all AP series


G) Sum of any N consecutive integers is always divisible by N for N being ODD (Not for even)

So the average of N consecutive integers is an integer for N being ODD

H) Product of n consecutive integers is always is always divisible by n!

Anything else ?


Regards
Stone Cold


Hi Bro, You have made a comprehensive collection:

Just to top a few,

1. Series 2,4,6.........2836

No of elements in this series (N) = ((L - A)/D) + 1

L - last term - 2836
A - First term - 2
D - Common Difference - 2

N = ((2836-2)/2)+1 = 1418 elements

2. Consider three elements : 1,2,3

Arithmetic mean = (1+2+3)/3 = 2

geometric mean = nth root(a*b*....n) = cube root(1*2*3) = cube root(6) = 1.817

Cheers
Balaji
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Re: Arithmetic Progression  [#permalink]

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New post 26 Nov 2019, 21:04
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Re: Arithmetic Progression   [#permalink] 26 Nov 2019, 21:04
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