Question

Чи є членом арифметичноі прогресіі -10; -5,5; -1; 3,5...число 71? Помогите SOS!!!

Answer 1

A1=-10 a2=-5
d=a2-a1=-5+10=5
an=-10+5(n-1)
-10+5(n-1)=71
5(n-1)=71+10
5(n-1)=81
n-1=81:5
n-1=16,2
n=16,2+1
n=17,2∉z
не является

a1=-1  a2=3
d=3+1=4
-1+4(n-1)=71
4(n-1)=71+1
4(n-1)=72
n-1=72:4
n-1=18
n=18+1
n=19
a19=71
является

Answer 2

Checking Arithmetic Progression for the Number 71

To determine if the number 71 is a member of the arithmetic progression with the given terms, we can use the formula for the nth term of an arithmetic progression:

nth term = a + (n-1)d

Where: - a = the first term - n = the term number - d = the common difference

In this case, the first term (a) is -10, and the common difference (d) is 5.5 - (-10) = 15.5.

Let's calculate the term number (n) for the number 71 using the given terms and the common difference.

Calculating the Term Number for 71

Using the formula for the nth term of an arithmetic progression, we can calculate the term number (n) for the number 71:

71 = -10 + (n-1) * 15.5

Solving for n: 71 + 10 = (n-1) * 15.5 81 = 15.5n - 15.5 96.5 = 15.5n n = 96.5 / 15.5 n ≈ 6.23

The term number (n) for the number 71 is approximately 6.23. Since the term number must be a positive integer, 71 is not a member of the given arithmetic progression.

Therefore, 71 is not a member of the arithmetic progression -10, -5.5, -1, 3.5...