Question

Укажите номер данного члена геометрической прогрессии 4; 12; 36; ...если bn= 972.С РЕШЕНИЕМ ПЖЛСТ.

Answer 1

Решение смотри на фотографии

Answer 2

Finding the nth Term of a Geometric Progression

To find the nth term of a geometric progression, we can use the formula:

a_n = a_1 * r^(n-1)

Where: - a_n = the nth term - a_1 = the first term - r = the common ratio - n = the term number

In this case, we are given that a_1 = 4 and a_n = 972. We need to find the value of n when a_n = 972.

Calculating the Term Number

Using the formula a_n = a_1 * r^(n-1), we can rearrange it to solve for n:

n = log(a_n / a_1) / log(r) Given that a_1 = 4 and a_n = 972, we need to find the common ratio r to calculate the term number n.

Finding the Common Ratio

To find the common ratio r, we can use the given terms of the geometric progression: 4, 12, 36.

r = term(n) / term(n-1)

r = 12 / 4 = 3

Now that we have the common ratio r = 3, we can calculate the term number n using the formula:

n = log(972 / 4) / log(3)

Calculating the Term Number

Let's calculate the term number n using the given values:

n = log(972 / 4) / log(3) n ≈ 5.0

So, the term number of the given member of the geometric progression 4, 12, 36, ... when a_n = 972 is approximately 5.