Question

1; -5; -11 чи є число -46 членами арифметичної прогресії ​

Answer 1

Ответ:

Пошаговое объяснение:

a1=1,  d=-5-1,  d=-6,  an=a1+d(n-1),  -46=1-6(n-1),  -47=-6n+6,  -53=-6n,

n=53/6 ( это число не натуральное),  ответ: нет

Answer 2

To determine if -46 is a member of the arithmetic progression, we need to find the common difference of the arithmetic progression first. An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant.

Given the sequence: 1; -5; -11; ...

To find the common difference (d), we can subtract the second term from the first term:

d = (-5) - 1 = -6

Now, we can check if -46 is a member of the arithmetic progression by using the formula for the nth term of an arithmetic progression:

nth term = a + (n - 1) * d

where: a = the first term of the sequence d = the common difference n = the position of the term we want to find

Let's calculate the position (n) of -46 in the arithmetic progression:

-46 = 1 + (n - 1) * (-6)

Now, let's solve for n:

-46 = 1 - 6n + 6

-46 - 1 + 6 = -6n

-39 = -6n

n = -39 / -6

n = 6.5

Since n is not a whole number, it means that -46 is not a member of the arithmetic progression, because arithmetic progressions consist of integer positions. So, -46 is not a part of the given arithmetic progression 1; -5; -11.