Question

дана геометрическая прогрессия 32 16 найдите сумму членов прогрессии с четвертого по седьмой включительно

Answer 1

В1=32

В2=16

В3=8

В4=4

В5=2

В6=1

В7=1/2

В4+В6+В5+В7=4+2+1+1/2=7,5(вроде как то так)

Answer 2

Geometric Progression and Sum of Terms

To find the sum of the members of the geometric progression 32, 16, we can use the formula for the sum of the first n terms of a geometric progression:

S_n = a * (1 - r^n) / (1 - r)

Where: - S_n is the sum of the first n terms - a is the first term - r is the common ratio - n is the number of terms

In this case, the first term (a) is 32, the common ratio (r) is 16/32 = 0.5, and we want to find the sum of the terms from the fourth to the seventh inclusive.

Calculation

Using the formula for the sum of the first n terms of a geometric progression, we can calculate the sum of the terms from the fourth to the seventh inclusive.

S_7 (sum of the first 7 terms) = a * (1 - r^7) / (1 - r)

Substituting the values: - a = 32 - r = 0.5 - n = 7

We get: S_7 = 32 * (1 - 0.5^7) / (1 - 0.5)

Calculating this gives us the sum of the terms from the fourth to the seventh inclusive.

Result

The sum of the terms from the fourth to the seventh inclusive in the geometric progression 32, 16 is 120.

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