Question

ДАМ 20 БАЛЛОВ Пусть an есть арифметическая прогрессия. Если a1=10, 2 и a3=9, 2. С помощью характеристического свойства найдите a2. Какой член последовательности будет наименьшим положительным числом? ​

Answer 1

Ответ:

Объяснение:

a₂=(a₁+a₃)/2=(10+9,2)/2=9,6

d=a₂-a₁=9,6-10=-0,4

Для нахождения наименьшего положительного члена решим неравенство с энным членом прогрессии

an=a₁+d(n-1)>0

10-0,4(n-1)>0

n<(10/0,4)+1

n<26

a₂₅=a₁+24d=10-0,4*24=0,4

25 член последовательности будет наименьшим положительным числом

Для проверки

a₂₆=a₁+25d=10-0,4*25=0

a₂₇a₁+26d=10-0,4*26=-0,4

Answer 2

Finding the Value of a2 in an Arithmetic Progression

To find the value of a2 in an arithmetic progression, we can use the characteristic property of an arithmetic progression.

In this case, we are given that a1 = 10.2 and a3 = 9.2.

The characteristic property states that the common difference between consecutive terms in an arithmetic progression is constant.

To find a2, we can use the formula:

a2 = a1 + (2 - 1) * d

where d is the common difference.

Since a1 = 10.2 and a3 = 9.2, we can subtract a1 from a3 to find the common difference:

d = a3 - a1 = 9.2 - 10.2 = -1

Now we can substitute the values into the formula to find a2:

a2 = 10.2 + (2 - 1) * (-1) = 10.2 - 1 = 9.2

Therefore, a2 in the arithmetic progression is 9.2.

Finding the Smallest Positive Number in the Sequence

To find the smallest positive number in the sequence, we need to determine the pattern of the arithmetic progression.

Since the common difference is -1, we can see that each term is decreasing by 1.

Starting from a1 = 10.2, the sequence would be:

10.2, 9.2, 8.2, 7.2, ...

We can observe that the sequence continues indefinitely, decreasing by 1 with each term.

Since the sequence continues indefinitely, there is no smallest positive number in the sequence. The terms in the sequence are all negative or zero.

Therefore, there is no smallest positive number in the given arithmetic progression.

I hope this helps! Let me know if you have any further questions.