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 burgess July 28th, 2014 10:58 PM

Some formulas of Arithmetic progression/series

An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Example: 2,4,6,8,10…..

Arithmetic Series : The sum of the numbers in a finite arithmetic progression is called as Arithmetic series.
Example: 2+4+6+8+10…..

nth term in the finite arithmetic series

Suppose Arithmetic Series a1+a2+a3+…..an
Then nth term an=a1+(n-1)d

Where
a1- First number of the series
an- Nth Term of the series
n- Total number of terms in the series
d- Difference between two successive numbers

Sum of the total numbers of the arithmetic series

Sn=n/2*(2*a1+(n-1)*d)

Where
Sn – Sum of the total numbers of the series
a1- First number of the series
n- Total number of terms in the series
d- Difference between two successive numbers

Example:

Find n and sum of the numbers in the following series 3 + 6 + 9 + 12 + x?
Here a1=3, d=6-3=3, n=5

x= a1+(n-1)d = 3+(5-1)3 = 15

Sn=n/2*(2a1+(n-1)*d)
Sn=5/2*(2*3+(5-1)3)=5/2*18 = 45

I hope the above formulae are helpful to solve your math problems.

 CRGreathouse July 29th, 2014 06:44 AM

In a related note, you may find the gp command sumformal() useful. Let's say you want to find the sum of \$3n^2-2n\$. Just type
Code:

`sumformal(3*n^2-2*n)`
and you get
Code:

`n^3 + 1/2*n^2 - 1/2*n`
in which you can substitute whatever values you need (either by hand or with gp's subst() command).

 burgess August 6th, 2014 03:29 AM

Quote:
 Originally Posted by CRGreathouse (Post 201718) In a related note, you may find the gp command sumformal() useful. Let's say you want to find the sum of \$3n^2-2n\$. Just type Code: `sumformal(3*n^2-2*n)` and you get Code: `n^3 + 1/2*n^2 - 1/2*n` in which you can substitute whatever values you need (either by hand or with gp's subst() command).
Thanks for your suggestion :)

 skipjack August 6th, 2014 09:58 AM

As the nth number is a1 + (n - 1)d, Sn = n(a1 + an)/2.

Note that (a1 + an)/2 is the median of the n numbers, and is the "middle" number of the series if n is odd.

It's slightly confusing to start by referring to a sequence of numbers and then keep switching between using the words "number" and "term".

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