Question

3.1. сумма 6-ого и 10-ого членов арифметической прогрессии равна 26. сумма первых 15 членов этой прогрессии равна? 3.2. если сумма 13-ого и 17-ого членов арифметической прогрессии равно 10, то чему равно сумма 1-ого, 15-ого и 29-ого членов? 3.3. в арифметической прогрессии сумма 3-ого, 7-ого, 14-ого и 18-ого членов равна 10. сумма первых 20 членов прогрессии равна? 4.1. арифметическая прогрессия содержит 10 членов. сумма членов, стоящих на чётных мечтах, равна 50, а на нечётных местах 35. 1-й член прогресси равен?

Answer 1

4.1 Сумма 10 членов 
S10 = (2a1 + d*(n-1)) * n / 2 = 50 + 35
(2a1 + 3*9) * 10 / 2 = 85
10a1 + 135 = 85 
10a1 = -50 
a1 = -5

Ответ: а1 = -5

Answer 2

3.1. Сумма 6-ого и 10-ого членов арифметической прогрессии равна 26. Сумма первых 15 членов этой прогрессии равна?

To find the sum of the first 15 terms of an arithmetic progression, we need to know the common difference and the first term of the progression. However, this information is not provided in the question. Therefore, it is not possible to determine the sum of the first 15 terms of the given arithmetic progression without additional information.

3.2. Если сумма 13-ого и 17-ого членов арифметической прогрессии равна 10, то чему равно сумма 1-ого, 15-ого и 29-ого членов?

To find the sum of the 1st, 15th, and 29th terms of an arithmetic progression, we need to know the common difference and the first term of the progression. However, this information is not provided in the question. Therefore, it is not possible to determine the sum of the 1st, 15th, and 29th terms of the given arithmetic progression without additional information.

3.3. В арифметической прогрессии сумма 3-ого, 7-ого, 14-ого и 18-ого членов равна 10. Сумма первых 20 членов прогрессии равна?

To find the sum of the first 20 terms of an arithmetic progression, we need to know the common difference and the first term of the progression. However, this information is not provided in the question. Therefore, it is not possible to determine the sum of the first 20 terms of the given arithmetic progression without additional information.

4.1. Арифметическая прогрессия содержит 10 членов. Сумма членов, стоящих на чётных местах, равна 50, а на нечётных местах 35. 1-й член прогрессии равен?

Let's denote the first term of the arithmetic progression as 'a' and the common difference as 'd'. We are given that the sum of the terms at even positions is 50 and the sum of the terms at odd positions is 35.

The sum of the terms at even positions can be calculated using the formula for the sum of an arithmetic series:

Sum of terms at even positions = (number of terms / 2) * (2 * a + (number of terms - 1) * d)

Substituting the given values, we have:

50 = (10 / 2) * (2 * a + (10 - 1) * d) 50 = 5 * (2 * a + 9d) 10 * a + 45 * d = 50

Similarly, the sum of the terms at odd positions can be calculated using the same formula:

Sum of terms at odd positions = (number of terms / 2) * (2 * a + (number of terms - 1) * d)

Substituting the given values, we have:

35 = (10 / 2) * (2 * a + (10 - 1) * d) 35 = 5 * (2 * a + 9d) 10 * a + 45 * d = 35

We now have a system of two equations with two variables (a and d). Solving this system of equations will give us the values of a and d, which will allow us to find the first term of the arithmetic progression.

Unfortunately, the system of equations cannot be solved without additional information. The given information is not sufficient to determine the value of the first term (a) of the arithmetic progression.