CÂRSTOIU ANDA IOANA, VOICU ALEXANDRA, class XII B

In mathematics, the progression is a sequence of numbers derived from one another by following certain rules. The most commonly used are arithmetic progression and geometric progression. Each feature has a specific job (at which the previous number of string and a constant), adding in the case of arithmetic progressions and multiplying in the case of geometry.

Definition: A sequence of numbers where each term, starting with the second, is obtained from the previous one by adding the same number. Finite arithmetic progression is characterized by a constant difference between any two consecutive terms. They are like a 1, a 2,..., a n or a 1, a 1 + r, a 1 + 2r,..., a 1 + (n-1)r where :  n is the number of elements in the progression,  a k = a 1 + (k - 1)r, for all k between 1 and n, called the general formula.  r is ration : r = a k - a k-1 called recursion formula.  The amount of the first n numbers in a finite arithmetic progression can be calculated as follows: This formula was found by Gauss and since the time when he was in middle school. HEREHERE you can find properties of the arithmetic progressions and examples, and exercises HERE.HERE.

Definition: A string of numbers whose first term is nonzero, and each of its term, since the second is obtained by multiplying the previous one with the same nonzero number. Typical geometric progressions is that the relationship between any two consecutive terms is constant, this ratio is called progression ratio.  b k = b k-1. q =... = b 1. q k-1  The amount of the first n 'numbers in a progression is  S n = b 1. (1 + q + q q n - 1 ) = b 1. (q n - 1) / (q - 1), if q 1, otherwise S n = n. b 1. HEREHERE you can find properties and examples of geometric progression.