Question

Найдите сумму первых восьми членов арифметической прогрессии (Хn): 5,5; 6,3; ... . 9 класс. Прошу отвечать пользователей, хорошо разбирающихся в алгебре. Пожалуйста, подробное решение или объяснение, чтобы понять...

Answer 1

Для решения этой задачи есть два способа:
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Answer 2

Calculating the Sum of the First Eight Terms of an Arithmetic Progression

To find the sum of the first eight terms of the arithmetic progression, we can use the formula for the sum of the first n terms of an arithmetic progression:

Sum of n terms (S_n) = n/2 * (a₁ + a_n)

Where: - n = number of terms - a₁ = first term - a_n = nth term

In this case, the given arithmetic progression is: 5.5, 6.3, ...

Let's calculate the sum of the first eight terms using this formula.

Calculation

We need to find the first term (a₁) and the eighth term (a₈) of the arithmetic progression to use in the formula.

The common difference (d) of the arithmetic progression can be found by subtracting the first term from the second term: d = 6.3 - 5.5

Now, we can find the first term (a₁) by using the formula: a₁ = 5.5

The eighth term (a₈) can be found using the formula for the nth term of an arithmetic progression: a₈ = a₁ + (n - 1)d

Substitute the values we have: a₈ = 5.5 + 7d

Now, we can calculate the sum of the first eight terms using the formula: S₈ = 8/2 * (a₁ + a₈)

Let's calculate the sum using these values.

Result

The sum of the first eight terms of the given arithmetic progression is: S₈ = 8/2 * (5.5 + (5.5 + 7d))

This will give us the sum of the first eight terms.