_02a_Arithmetic_Progression Namespace Reference

Summing an Arithmetic Progression. More...

Functions
def	S (n, a1, d)
	Calculates the sum of the first n terms of an Arithmetic Progression. More...
def	Sp (n, a1, d)
	Calculates the sum of the first n terms of an Arithmetic Progression. More...
def	main ()

Detailed Description

Summing an Arithmetic Progression.

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.

For instance, the sequence 3, 5, 7, 9, 11, 13... is an arithmetic progression with common difference d=2, and first element a1=3.

Author

Paulo Roma

Since

08/04/2007

See also

http://en.wikipedia.org/wiki/Arithmetic_series

Function Documentation

main()

def _02a_Arithmetic_Progression.main

(

)

References _01d_dec2bin.input, validateRoman.raw_input, S(), and Sp().

S()

def _02a_Arithmetic_Progression.S	(		n,
			a1,
			d
	)

Calculates the sum of the first n terms of an Arithmetic Progression.

Parameters

n	an index of a term of the progression.
a1	first term of the sequence.
d	difference between to consecutive terms.

Returns

sum of the first n terms: \(S(n,a_{1},r) = \frac{n}{2}(2a_{1} + (n-1)d).\)

Referenced by main().

Sp()

def _02a_Arithmetic_Progression.Sp	(		n,
			a1,
			d
	)

Calculates the sum of the first n terms of an Arithmetic Progression.

Parameters

n	an index of a term of the progression.
a1	first term of the sequence.
d	difference between to consecutive terms.

Returns

a string with all terms of the progression, until \(a_n\), separated by "+" and "=" to its sum: "1 + 4 + 7 + 10 + 13 + 16 + 19 = 70".

Referenced by main().