Question

(bn)-геометрическая прогрессия, знаменатель прогрессии равен 1/2, b1= -8 найдите сумму первых шести её членов. Распишите пожалуйста,просто ответ не нужен.

Answer 1

Неужели так сложно поискать в интернете инфу, если не помнишь (или не знаешь) формулу?

Формула суммы n-первых членов геометрической прогрессии:

$S_n= \frac{b_1*(1-q^n)}{1-q}$

Ну и подставляем в формулу всё, что дано в задании:

$S_6= \frac{-8*(1- (\frac{1}{2})^6)}{1- \frac{1}{2}}= \frac{-8*(1- \frac{1}{64} )}{ \frac{1}{2}}= \frac{-8* \frac{63}{64} }{ \frac{1}{2}}= \frac{ -\frac{63}{8} }{ \frac{1}{2}}=- \frac{63}{8}: \frac{1}{2} =\\ =-\frac{63}{8}* \frac{2}{1} =- \frac{63}{4}=- 15 \frac{3}{4} =-15,75$

Answer 2

Geometric Progression with a Common Ratio of 1/2

A geometric progression is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, the common ratio is 1/2.

Let's find the sum of the first six terms of this geometric progression.

Finding the First Term (b1)

The first term of the geometric progression is denoted as b1. In this case, b1 is given as -8.

Finding the Sum of the First Six Terms

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

S6 = b1 * (1 - r^6) / (1 - r)

Where: - S6 is the sum of the first six terms - b1 is the first term of the geometric progression - r is the common ratio

Substituting the given values into the formula, we have:

S6 = -8 * (1 - (1/2)^6) / (1 - 1/2)

Simplifying the equation:

S6 = -8 * (1 - 1/64) / (1/2)

S6 = -8 * (63/64) / (1/2)

S6 = -8 * (63/64) * (2/1)

S6 = -8 * 63

S6 = -504

Therefore, the sum of the first six terms of the geometric progression is -504.

Please note that the sources used for this response are not available.