Question

ДАЮ СТО БАЛЛОВ!!!!!!!!!!!!!!!!!!!! c(n) Геометрическая прогрессия. Найдите её знаменатель если c15=27 и c18=-1 ДАЮ СТО БАЛЛОВ!!!!!!!!!!!!!!!!!!!!

Answer 1

пусть c1- первый член геометрическоц прогрессии, а q - ее знаменатель, тогда

$c_{15}=c_1•q¹⁴ \\ c_{18}= c_1•q¹⁷$

разделим второе на первое:

$\frac{c_{18}}{c_{15}} = {q}^{17 - 14} \\ {q}^{3} = \frac{c_{18}}{c_{15}} = - \frac{1}{27}$

откуда

$q = \sqrt[3]{ - \frac{1}{27} } = - \frac{1}{3}$

ответ :

q= -⅓

Answer 2

Ответ:

Пошаговое объяснение:

b15 = b1 *q^14

b18 = b1 *q^17

27 = b1 * q^14

-1 = b1 * q^17  

нужно разделить второе уравнение на первое и получим

-1/27 = q^3

q^3 = - 1/27

q = - 1/3

Answer 3

Geometric Progression and Common Ratio

In a geometric progression, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. The formula for the n-th term of a geometric progression is given by:

c(n) = c(1) * r^(n-1)

Where: - c(n) is the n-th term - c(1) is the first term - r is the common ratio - n is the term number

Finding the Common Ratio

Given: - c(15) = 27 - c(18) = -1

We can use these values to find the common ratio (r).

Using the formula c(n) = c(1) * r^(n-1), we can set up the following equations:

c(15) = c(1) * r^(15-1) = 27 c(18) = c(1) * r^(18-1) = -1

We can use these equations to solve for the common ratio (r).

Calculating the Common Ratio

To find the common ratio (r), we can use the given values of c(15) and c(18) to form the following equations:

c(1) * r^14 = 27 c(1) * r^17 = -1

Dividing the second equation by the first, we get:

(c(1) * r^17) / (c(1) * r^14) = -1 / 27 r^3 = -1 / 27

Taking the cube root of both sides, we find:

r = -1 / 3

Conclusion

The common ratio (r) for the given geometric progression is -1/3.