Question

Скільки додатних членів містить арифметична прогресія,якщо а1=41;а2=32.​

Answer 1

Объяснение:

найдём разность:

d = a2-a1

d = 32 - 41 = -9

вспомним формулу нахождения n-ного члена арифметической прогрессии:

$a_{n} = a_{1} + d(n - 1)$

теперь вместо an подставим ноль и получим уравнение относительно n:

$0 = a_{1} + d(n - 1) \\ 41 - 9(n - 1) = 0 \\ 9(n - 1) = 41 \\ 9n - 9 = 41 \\ 9n = 50 \\ n = 5.(5)$

но т.к. n принадлежит множеству целых чисел, то n = 5, проверим пятый n-ный член по формуле выше

$a_{5} = a_{1} + (5 - 1)d \\ a_{5} = 41 + 4 \times ( - 9) \\ a_{5} = 41 - 36 \\ a_{5} = 5$

значит, всего 5 положительных членов арифметической прогрессии

Answer 2

Number of Positive Terms in an Arithmetic Progression

In an arithmetic progression, the terms are generated by adding a constant difference to the preceding term. The formula to find the nth term of an arithmetic progression is given by:

a_n = a_1 + (n - 1)d

Where: - a_n is the nth term - a_1 is the first term - n is the term number - d is the common difference

Given: - a_1 = 41 - a_2 = 32

We can use these values to find the common difference (d):

a_2 = a_1 + d 32 = 41 + d d = -9

Now, we can find the nth term where the term becomes non-positive:

a_n = 41 + (n - 1)(-9) a_n = 41 - 9n + 9 a_n = 50 - 9n

To find the number of positive terms, we need to solve for n when a_n becomes non-positive:

50 - 9n <= 0 -9n <= -50 n >= 50/9 n ≈ 5.56

Since n must be a positive integer, the number of positive terms in the arithmetic progression is 5.