Geometric progression

A geometric progression is a numerical sequence in which all its terms are arranged in an order that follows a certain pattern. The formula of geometric progression determines that each subsequent number will be obtained by multiplying the previous one by the denominator of the progression - a constant number that does not change its value within one sequence. b_n=b₁ q^(n-1)

Depending on the denominator of the progression, the listed terms of the geometric progression can give a different type of series. If the denominator is a positive number greater than 1 (k > 1), then it will increase the value of each subsequent number. Such a progression will monotonically increase throughout the series. If the denominator is positive but between 0 and 1 (0 < k < 1), then it will decrease the value of each subsequent term each time, and such a progression will be called an infinitely decreasing geometric progression.

If for an all-increasing sequence, it is only possible to find the sum of the first terms of the geometric progression, then the sum of the terms of an infinitely decreasing progression will be equal to a specific numerical value that the calculator can calculate. The third case is represented by a negative denominator (k < 0), then the progression becomes alternating, i.e., the first terms of the geometric progression determine the order of signs for the entire sequence of numbers. Both the denominator of the geometric progression and the first term of the geometric progression by definition cannot be equal to zero.

There are only a few formulas for geometric progression, from which all necessary solutions for specific tasks can be derived:

• Formula of the first term of geometric progression;

• Formula nof the term of geometric progression;

• Formula of the sum of the first terms of geometric progression;

• Formula of the sum of an infinitely decreasing geometric progression;

• Formula of the denominator of geometric progression.

Thus, if a geometric progression is specified by at least two parameters from all those presented above, it is possible to find any of all other variables for it.