Download PROGRESII ARITMETICE, PROGRESII GEOMETRICE

CÂRSTOIU ANDA IOANA, VOICU ALEXANDRA, class XII B
ARITHMETIC PROGRESSIONS,
GEOMETRIC PROGRESSION
MATHEMATICAL PROGRESSION
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.
ARITHMETIC PROGRESSIONS
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 a1, a2, ..., an or a1 , a1 + r , a1 + 2r , ... , a1 +
(n-1)r where:
 n is the number of elements in the progression,
 ak = a1 + (k - 1)r , for all k between 1 and n, called the general formula.
 r is ration : r = ak - ak-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.
HERE you can find properties of the arithmetic progressions and examples, and
exercises HERE.
GEOMETRIC PROGRESSIONS
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.
 bk = bk-1 . q = ... = b1 . qk-1
 The amount of the first n 'numbers in a progression is
 Sn = b1 . (1 + q + q2 + ... + qn - 1) = b1 . (qn - 1) / (q - 1), if q 1,
otherwise Sn = n . b1.
HERE you can find properties and examples of geometric progression.