Question

Послідовність an арифметична прогресія А1 = 20, d = -3. Чи є членом цієї прогресії число -90?​

Answer 1

Ответ: не містить

Пошаговое объяснение:
d=-3
An=20
20+(-3)(n-1)=-90
20-3n+3=-90
-3n=-90-20-3
-3n=-113
n=37,6
(Щоб містило треба щоб n дорівнювала цілому числу)

Answer 2

Arithmetic Progression with a1 = 20 and d = -3

An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, we have an arithmetic progression with the first term (a1) equal to 20 and the common difference (d) equal to -3.

To determine if a number is a member of this arithmetic progression, we can use the formula for the nth term of an arithmetic progression:

an = a1 + (n - 1) * d

where an represents the nth term of the progression.

Let's substitute the given values into the formula:

an = 20 + (n - 1) * (-3)

Now, we can check if -90 is a member of this arithmetic progression by solving for n:

-90 = 20 + (n - 1) * (-3)

Simplifying the equation:

-90 = 20 - 3n + 3

-90 - 20 - 3 = -3n

-113 = -3n

Dividing both sides of the equation by -3:

n = 113 / 3

After evaluating the expression, we find that n is not an integer. Therefore, -90 is not a member of this arithmetic progression.

Please let me know if there is anything else I can help you with!