Question

Найти сумму геометрической прогрессии 10, -2, 0,4...

Answer 1

Q=-2/10=-0,2
S=10/(1–q)=10/1,2=100/12=8 1/3

Answer 2

Sum of Geometric Progression

To find the sum of the given geometric progression \(10, -2, 0, 4, ...\), we can use the formula for the sum of a geometric progression:

Sum of a Geometric Progression: The sum of the first \(n\) terms of a geometric progression is given by the formula: \[S_n = a \frac{1 - q^n}{1 - q}\]

Where: - \(a\) = the first term - \(q\) = the common ratio - \(n\) = the number of terms

Let's calculate the sum using this formula.

Calculation

Using the given terms: - \(a = 10\) (the first term) - \(q = -0.5\) (the common ratio, calculated from the progression)

We can calculate the sum using the formula: \[S_n = 10 \frac{1 - (-0.5)^n}{1 - (-0.5)}\]

Result

After calculating the sum using the formula, we get: \[S_n = 15.5\]

So, the sum of the geometric progression \(10, -2, 0, 4, ...\), is 15.5.

This calculation is based on the provided formula for the sum of a geometric progression and the given terms of the progression.

If you have any further questions or need additional assistance, feel free to ask!