Question

S6-S5=-128 q=-2 B8-? ГЕОМЕТРИЧЕСКАЯ ПРОГРЕССИЯ

Answer 1

Ответ: b8=-513

Объяснение:

Answer 2

To find the missing term in the geometric progression, we need to determine the common ratio (q) and one of the terms. In this case, we know that S6 - S5 = -128 and q = -2.

The formula for the sum of a geometric progression is given by:

Sn = a * (1 - q^n) / (1 - q),

where Sn is the sum of the first n terms, a is the first term, and q is the common ratio.

Given that S6 - S5 = -128, we can substitute the values into the formula:

a * (1 - q^6) / (1 - q) - a * (1 - q^5) / (1 - q) = -128.

Now, let's substitute q = -2 and solve for a:

a * (1 - (-2)^6) / (1 - (-2)) - a * (1 - (-2)^5) / (1 - (-2)) = -128,

a * (1 - 64) / 3 - a * (1 - 32) / 3 = -128,

a * (-63) / 3 - a * (-31) / 3 = -128,

-63a - 31a = -384.

-94a = -384,

a = -384 / -94,

a ≈ 4.0851.

Now that we have the value of the first term (a), we can find the missing term B8.

B8 = a * q^(8-1),

B8 = 4.0851 * (-2)^7,

B8 = 4.0851 * (-128),

B8 ≈ -523.3952.

Therefore, the missing term in the geometric progression is approximately -523.3952.