Question

Является ли число 25 членом арифметической прогрессии -3; 4; 11; ...? Если является, то укажите его номер

Answer 1

Пусть 25 = аn, найдём d. d= 4-(-3) = 7
an = a1 + (n-1) ·d
25 = -3 +(n - 1)·7
25 = -3 +7n -7
25 = -10 + 7n
7n = 35
n = 5
Ответ: 25= а5

Answer 2

Checking if 25 is a Member of an Arithmetic Progression

To determine if 25 is a member of the arithmetic progression -3, 4, 11, ..., we can use the formula for the nth term of an arithmetic progression:

nth term (Tn) = 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 -3, and the common difference (d) is 7 (the difference between consecutive terms).

Using the formula, we can calculate the term number (n) for the value 25.

Tn = -3 + (n - 1) * 7 = 25

Solving for n: 7n - 7 = 28 7n = 35 n = 5

So, the term number for the value 25 in the arithmetic progression -3, 4, 11, ... is 5.