Question

Даю 30балов срочно!!!!очень!!!!Первый член геометрической прогрессии равен 4 Четвертый равен 16.найти сумму 10 первых членов И сумму 12 первых членов прогрессии​

Answer 1

Ответ:

сумма 10первых равен 100. А сумма 12первых равен 144.

Пошаговое объяснение:

10*10=100, 12*12=144

Answer 2

Given Information:

The first term of a geometric progression is 4, and the fourth term is 16.

Finding the Common Ratio:

To find the common ratio of the geometric progression, we can use the formula:

nth term = a * r^(n-1)

where: - nth term is the term we want to find (in this case, the fourth term is 16) - a is the first term of the geometric progression (in this case, a = 4) - r is the common ratio of the geometric progression

Substituting the given values into the formula, we have:

16 = 4 * r^(4-1)

Simplifying the equation, we get:

16 = 4 * r^3

Dividing both sides of the equation by 4, we have:

4 = r^3

Taking the cube root of both sides, we find:

r = ∛4

Therefore, the common ratio of the geometric progression is ∛4.

Finding the Sum of the First 10 Terms:

To find the sum of the first 10 terms of the geometric progression, we can use the formula for the sum of a geometric series:

Sum = a * (1 - r^n) / (1 - r)

where: - Sum is the sum of the terms we want to find - a is the first term of the geometric progression (in this case, a = 4) - r is the common ratio of the geometric progression (in this case, r = ∛4) - n is the number of terms we want to sum (in this case, n = 10)

Substituting the given values into the formula, we have:

Sum = 4 * (1 - (∛4)^10) / (1 - ∛4)

Calculating the value, we find:

Sum of the first 10 terms = 4 * (1 - (∛4)^10) / (1 - ∛4)

Finding the Sum of the First 12 Terms:

To find the sum of the first 12 terms of the geometric progression, we can use the same formula as above, but with n = 12:

Sum = 4 * (1 - (∛4)^12) / (1 - ∛4)

Calculating the value, we find:

Sum of the first 12 terms = 4 * (1 - (∛4)^12) / (1 - ∛4)

Please note that the exact numerical values of the sums will depend on the value of ∛4, which is approximately 1.5874.