Question

Найдите первый член арифметической прогрессии ,cостоящий из восьми членов если ее сумма равна 36,а последний член равен 5.Срочно,заранее спасибо!!!

Answer 1

S8=(a1+a8)*8/2
36=(a1+5)*4
a1+5=9
a1=9-5=4

Answer 2

Finding the First Term of an Arithmetic Progression

To find the first term of an arithmetic progression with a sum of 36 and a last term of 5, we can use the formula for the sum of an arithmetic series:

Sum of an Arithmetic Series Formula: The sum of the first n terms of an arithmetic series is given by the formula: S = (n/2)(a1 + an), where: - S = sum of the series - n = number of terms - a1 = first term - an = last term

We are given that the sum of the series is 36 and the last term is 5. We need to find the first term, a1.

Calculating the First Term

Using the formula for the sum of an arithmetic series, we can solve for the first term, a1:

36 = (n/2)(a1 + 5)

We also know that the last term, an, is 5.

Solving for the Number of Terms

To find the number of terms, n, we can use the formula for the nth term of an arithmetic sequence:

nth Term of an Arithmetic Sequence Formula: The nth term of an arithmetic sequence is given by the formula: an = a1 + (n - 1)d, where: - an = nth term - a1 = first term - n = number of terms - d = common difference

In this case, we know that the last term, an, is 5. We also know that the first term, a1, is what we are trying to find. The common difference, d, can be calculated as the difference between the last term and the first term.

Conclusion

By using the given information and the formulas for the sum and nth term of an arithmetic series, we can calculate the first term of the arithmetic progression.