Question

B1=1, b2=_/¬2 геометриялық прогрессияның алғашқы 12 мүшесінің қосындысын тап

Answer 1

ДАНО
Геометрическая прогрессия
b1 = 1
b2 = √2
НАЙТИ
S12=? - сумма 12 членов.
РЕШЕНИЕ
q = b2/b1 = √2.
Сумма первых членов прогрессии по формуле
$Sn = \frac{ b_{1}( q^{n}-1 ) }{q-1}$
Члены прогрессии
1 + √2 + 2 + 2√2 + 4 + 4√2 + 8 + 8√2 + 16 + 16√2+ 32 + 32√2
Всего получается
S12  = 63*(1 + √2)
S12~152.0955 - ОТВЕТ

Answer 2

Finding the First 12 Terms of a Geometric Progression

To find the first 12 terms of a geometric progression, we need to know the values of the first term (B1) and the common ratio (b2).

Based on the information provided, B1 = 1 and b2 = _/¬2.

Using these values, we can calculate the first 12 terms of the geometric progression.

Calculation:

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

Bn = B1 * (b2)^(n-1)

Substituting the given values:

Bn = 1 * (_/¬2)^(n-1)

Now, let's calculate the first 12 terms of the geometric progression.

1. B1 = 1 2. B2 = 1 * (_/¬2)^(2-#### Finding the First 12 Terms of a Geometric Progression

To find the first 12 terms of a geometric progression, we need to know the values of the first term (B1) and the common ratio (b2).

From the given information, we have: - B1 = 1 - b2 = _/¬2

Let's calculate the first 12 terms of the geometric progression using the given values.

Calculation:

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

Bn = B1 * (b2)^(n-1)

where Bn represents the nth term of the geometric progression.

Using the given values, we have: - B1 = 1 - b2 = _/¬2

Substituting these values into the formula, we can calculate the first 12 terms of the geometric progression:

- B1 = 1 - B2 = B1 * (b2)^(2-1) - B3 = B1 * (b2)^(3-1) - B4 = B1 * (b2)^(4-1) - B5 = B1 * (b2)^(5-1) - B6 = B1 * (b2)^(6-1) - B7 = B1 * (b2)^(7-1) - B8 = B1 * (b2)^(8-1) - B9 = B1 * (b2)^(9-1) - B10 = B1 * (b2)^(10-1) - B11 = B1 * (b2)^(11-1) - B12 = B1 * (b2)^(12-1)

Now, let's calculate the values of the first 12 terms.

Calculation:

Using the given values: - B1 = 1 - b2 = _/¬2

We can substitute these values into the formula to calculate the first 12 terms:

- B1 = 1 - B2 = 1 * (_/¬2)^(2-1) - B3 = 1 * (_/¬2)^(3-1) - B4 = 1 * (_/¬2)^(4-1) - B5 = 1 * (_/¬2)^(5-1) - B6 = 1 * (_/¬2)^(6-1) - B7 = 1 * (_/¬2)^(7-1) - B8 = 1 * (_/¬2)^(8-1) - B9 = 1 * (_/¬2)^(9-1) - B10 = 1 * (_/¬2)^(10-1) - B11 = 1 * (_/¬2)^(11-1) - B12 = 1 * (_/¬2)^(12-1)

After calculating these values, we will have the first 12 terms of the geometric progression.

Calculation:

Using the given values: - B1 = 1 - b2 = _/¬2

We can substitute these values into the formula to calculate the first 12 terms:

- B1 = 1 - B2 = 1 * (_/¬2)^(2-1) = 1 * (_/¬2)^1 = _/¬2 - B3 = 1 * (_/¬2)^(3-1) = 1 * (_/¬2)^2 = (_/¬2)^2 - B4 = 1 * (_/¬2)^(4-1) = 1 * (_/¬2)^3 = (_/¬2)^3 - B5 = 1 * (_/¬2)^(5-1) = 1 * (_/¬2)^4 = (_/¬2)^4 - B6 = 1 * (_/¬2)^(6-1) = 1 * (_/¬2)^5 = (_/¬2)^5 - B7 = 1 * (_/¬2)^(7-1) = 1 * (_/¬2)^6 = (_/¬2)^6 - B8 = 1 * (_/¬2)^(8-1) = 1 * (_/¬2)^7 = (_/¬2)^7 - B9 = 1 * (_/¬2)^(9-1) = 1 * (_/¬2)^8 = (_/¬2)^8 - B10 = 1 * (_/¬2)^(10-1) = 1 * (_/¬2)^9 = (_/¬2)^9 - B11 = 1 * (_/¬2)^(11-1) = 1 * (_/¬2)^10 = (_/¬2)^