Question

B1=-2 q=3/4 Найти: Sn

Answer 1

$Sn = \frac{b1( {q}^{n} - 1) }{q - 1} = \frac{ - 2( {( \frac{3}{4}) }^{n} - 1) }{ \frac{3}{4} - 1 } = \frac{ - 2( \frac{ {3}^{n} }{ {4}^{n} } - 1) }{ - \frac{1}{4} } = 8( \frac{ {3}^{n} }{ {4}^{n} } - 1)$

Answer 2

To find the value of Sn, we need to know the specific formula for the sum of an arithmetic series. An arithmetic series is a sequence of numbers in which the difference between consecutive terms is constant. The sum of the first n terms of an arithmetic series can be calculated using the following formula:

Sn = n/2 * (a1 + an),

where: Sn is the sum of the first n terms, n is the number of terms, a1 is the first term of the series, and an is the nth term of the series.

Since we have the values of B1 and q, we can calculate the first term (a1) and the nth term (an) as follows:

a1 = B1 = -2, an = a1 + (n - 1) * q = -2 + (n - 1) * (3/4).

Now, we can substitute these values into the formula for Sn:

Sn = n/2 * (a1 + an) Sn = n/2 * (-2 + (-2 + (n - 1) * (3/4)))

Now, simplify the expression:

Sn = n/2 * (-2 - 2 + (3n - 3) * (3/4)) Sn = n/2 * (-4 + 3n - 3/4) Sn = n/2 * (3n - 19/4)

So, the formula for the sum of the first n terms of the given arithmetic series is Sn = n/2 * (3n - 19/4).