Question

Первый член геометрической прогрессии равен 2058 , а четвертый 6. Найдите знаменатель этой прогрессии ?

Answer 1

а1=2058

а4=6

а4=а1*q^3

а4/а1=q^3

q^3=343

q=7

q^3- q 3 степени

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

Finding the Common Ratio of a Geometric Progression

To find the common ratio (denoted by r) of a geometric progression when the first term is 2058 and the fourth term is 6, we can use the formula for the nth term of a geometric progression:

a_n = a_1 * r^(n-1)

where: - a_n is the nth term - a_1 is the first term - r is the common ratio - n is the term number

We are given: - a_1 = 2058 - a_4 = 6

We need to find r.

Calculating the Common Ratio

Using the formula for the nth term, we can set up the following equation for the fourth term:

a_4 = a_1 * r^(4-1)

Substitute the given values: 6 = 2058 * r^3

Now, solve for r: r^3 = 6 / 2058

Taking the cube root of both sides: r = (6 / 2058)^(1/3)

Calculating the Common Ratio

Using the given values, we can calculate the common ratio r:

r ≈ 0.1

So, the common ratio of this geometric progression is approximately 0.1.