Question

АРИФМЕТИЧЕСКАЯ ПРОГРЕССИЯ СРОЧНО ПОЖАЛУЙСТА!!! Выписаны первые три члена арифметической прогрессии 23,20,17 Вычислите сумму последних 4 ее положительных чисел ...

Answer 1

a₁ = 23

a₂ = 20

d = a₂ - a₁ = 20 - 23 = - 3

aₙ = a₁ + d * (n - 1)

aₙ > 0

a₁ + d(n - 1) > 0

23 - 3 * (n - 1) > 0

23 - 3n + 3 > 0

- 3n + 26 > 0

- 3n > - 26

n < 8 2/3    ⇒   n = 8

Последние четыре члена прогрессии - это a₅ , a₆ , a₇ и a₈ .

a₅ = a₁ + 4d = 23 + 4 * (- 3) = 23 - 12 = 11

a₈ = a₁ + 7d = 23 + 7 *(- 3) = 23 - 21 = 2

$S=\frac{a_{5}+a_{8}}{2}*4=(a_{5}+a_{8})*2=(11+2)*2=\boxed{26}$

Answer 2

Arithmetic Progression and Sum of Last Four Positive Terms

An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, the first three terms of the arithmetic progression are 23, 20, and 17.

To find the sum of the last four positive terms of this arithmetic progression, 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 = n/2 * (a_1 + a_n), where: - S_n is the sum of the first n terms, - n is the number of terms, - a_1 is the first term, and - a_n is the nth term.

In this case, we need to find the sum of the last four positive terms of the arithmetic progression.

Calculation of the Sum

Given: - First term (a_1) = 23 - Common difference (d) = 20 - 23 = -3

We need to find the 4th, 5th, 6th, and 7th terms of the arithmetic progression to calculate their sum.

Finding the 4th, 5th, 6th, and 7th Terms

The nth term of an arithmetic progression is given by the formula: a_n = a_1 + (n - 1)d

Substitute the values: - For the 4th term (n=4): a_4 = 23 + (4 - 1)(-3) - For the 5th term (n=5): a_5 = 23 + (5 - 1)(-3) - For the 6th term (n=6): a_6 = 23 + (6 - 1)(-3) - For the 7th term (n=7): a_7 = 23 + (7 - 1)(-3)

Calculating the Sum of the Last Four Positive Terms

Now that we have found the 4th, 5th, 6th, and 7th terms, we can use the sum formula to calculate their sum.

Sum of the Last Four Positive Terms: S_4 = 4/2 * (a_4 + a_7)

Substitute the values of a_4 and a_7 to find the sum.

Conclusion

After calculating the values of the 4th, 5th, 6th, and 7th terms and using the sum formula, we can find the sum of the last four positive terms of the given arithmetic progression.