Question

Выписаны три члена арифметической прогрессии: 10;6;2... Найдите 101-й член этой прогрессии

Answer 1

Arithmetic Progression

To find the 101st term of an arithmetic progression, we need to determine the common difference and the first term of the progression.

In this case, we are given three terms of the arithmetic progression: 10, 6, and 2.

To find the common difference, we can subtract the second term from the first term and the third term from the second term.

The common difference (d) is calculated as follows:

d = second term - first term = 6 - 10 = -4

Now that we have the common difference, we can find the first term (a) of the arithmetic progression.

To find the first term, we can use the formula:

a = first term - (n-1) * common difference

where n is the position of the term we want to find. In this case, we want to find the 101st term, so n = 101.

Substituting the values into the formula, we get:

a = 10 - (101-1) * (-4) a = 10 - 100 * (-4) a = 10 + 400 a = 410

Therefore, the first term of the arithmetic progression is 410.

To find the 101st term, we can use the formula:

nth term = first term + (n-1) * common difference

Substituting the values into the formula, we get:

101st term = 410 + (101-1) * (-4) 101st term = 410 + 100 * (-4) 101st term = 410 - 400 101st term = 10

Therefore, the 101st term of the arithmetic progression is 10.