Question

B1 =10 q=-1 S15-? (Геометрическая прогрессия )

Answer 1

Ответ:

S15=10

Объяснение:

B1 =10

q=-1

S15-?

(Геометрическая прогрессия )

B1 =10, B2 =-10, B3 =10..., B14 =-10, B15 =10

S1=10,                               S3= (B1+B2)+B3=S2+B3=0+10=10,... S15=S14+B15=10

S2=B1 +B2 =10-10=0,         S4=S3+B4=0-10=0,...         S14=0

Answer 2

To find the 15th term (S15) of a geometric progression (GP) with the first term (B1) of 10 and the common ratio (q) of -1, we can use the formula for the nth term of a GP:

Bn = B1 * q^(n-1)

where Bn is the nth term, B1 is the first term, q is the common ratio, and n is the term number.

In this case, we need to find S15, which represents the sum of the first 15 terms of the geometric progression. The formula for the sum of the first n terms of a geometric progression is given by:

Sn = B1 * (1 - q^n) / (1 - q)

where Sn is the sum of the first n terms.

Now, let's plug in the values:

B1 = 10 q = -1 n = 15

First, let's find the 15th term (B15):

B15 = B1 * q^(15-1) B15 = 10 * (-1)^14 B15 = 10 * 1 B15 = 10

Now, let's find the sum of the first 15 terms (S15):

S15 = B1 * (1 - q^15) / (1 - q) S15 = 10 * (1 - (-1)^15) / (1 - (-1)) S15 = 10 * (1 - (-1)) / (1 + 1) S15 = 10 * (1 + 1) / 2 S15 = 10 * 2 / 2 S15 = 10

So, the 15th term (B15) of the geometric progression is 10, and the sum of the first 15 terms (S15) is also 10.