Geometric Progression Example

The geometric progression It is how the process is called in which a series of numbers is obtained that are obtained through successive multiplication using a number that is called reason.

So the geometric progression It is how the set of numbers is known, in which depending on the first the others are obtained by multiplying by the same number constantly to obtain the next number.

The notation is as follows:

a = to the first term

r = common ratio

s = sum

n = number of terms

This progression has a formula to calculate the sum, which is obtained as follows:

Being "to"The first term the next term is obtained by multiplying a by" r "and so on, thus remaining like this:

a, ar, ar², ar³... ar^n-1

Geometric progression formula example:

 a, ar, ar², ar³,……

The following emerges:

s = a, ar, ar², ar³ +… + Ar^n-1

rs = ar + ar² + ar³ +… Ar^n-1+ arⁿ

rs - s = arⁿ-to

(r-1) s = (rn-1)

s = a (rn-1)

r-1

Noting that "r”Must be different from 1.

Examples of geometric progression:

2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048……

3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049,……

4, 16, 64, 256,……

5, 25, 125, 625, 3125,……

6, 36, 216, 1296, 7776, 46656,……

7, 49, 243, 2058, 12348,……

8, 64, 512, 4096, 32768,……

Here the first number is multiplied by itself, becoming the ratio number, and the rest of the numbers are raised in geometric form, obtaining the results progressively.

Exercises with geometric progression:

Geometric progression raising 25 with the number of reason 3:

25 = 25, 75, 225, 675, 2025, 6075, 18225,……

Geometric progression raising 12 with the number of reason 8:

12 = 12, 96, 768, 6144, 49152, 393216, 3145728,……

Geometric progression raising 4 with the number of reason 13:

4 = 4, 52, 676, 8 788,144 244, 1 485 172, 19 307 236, 250 994 068,……