Question

Найди закономерности , по которым составлены ряды чисел, и продолжи каждый из них на 4 числа . 298, 287, 265, 232, 188... 1280, 640, 320, 160, 80, ... 2,3,5,8,13,21,... 2) составь свои ряды, используя многозначные числа и другие закономерности.

Answer 1

298, 287, 265, 232, 188, 133, 67,
1280, 640, 320, 160, 80, 40, 20, 10,
2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

Answer 2

Finding Patterns in the Given Number Series

Let's analyze each number series and try to identify the patterns in order to continue them.

1. 298, 287, 265, 232, 188...

By observing the given series, we can see that each number is decreasing. The difference between consecutive terms seems to be decreasing as well. Let's calculate the differences between consecutive terms:

- Difference between 298 and 287: 298 - 287 = 11 - Difference between 287 and 265: 287 - 265 = 22 - Difference between 265 and 232: 265 - 232 = 33 - Difference between 232 and 188: 232 - 188 = 44

We can notice that the differences are increasing by 11 each time. Therefore, we can continue the series by subtracting 55 from the last term:

- 188 - 55 = 133 - 133 - 55 = 78 - 78 - 55 = 23

So, the next four terms of the series would be: 133, 78, 23, -32.

2. 1280, 640, 320, 160, 80...

In this series, each term is being divided by 2 to obtain the next term. Let's calculate the division for each consecutive pair of terms:

- 1280 ÷ 2 = 640 - 640 ÷ 2 = 320 - 320 ÷ 2 = 160 - 160 ÷ 2 = 80

Therefore, we can continue the series by dividing the last term by 2:

- 80 ÷ 2 = 40 - 40 ÷ 2 = 20 - 20 ÷ 2 = 10

So, the next four terms of the series would be: 40, 20, 10, 5.

3. 2, 3, 5, 8, 13, 21...

This series seems to follow the Fibonacci sequence, where each term is the sum of the two preceding terms. Let's calculate the sum for each consecutive pair of terms:

- 2 + 3 = 5 - 3 + 5 = 8 - 5 + 8 = 13 - 8 + 13 = 21

Therefore, we can continue the series by adding the last two terms:

- 13 + 21 = 34 - 21 + 34 = 55 - 34 + 55 = 89

So, the next four terms of the series would be: 34, 55, 89, 144.

4. 2, 3, 5, 8, 13, 21...

In this series, each term is obtained by adding the previous term to the square of its position in the series. Let's calculate the terms using this pattern:

- 2 + (1^2) = 2 + 1 = 3 - 3 + (2^2) = 3 + 4 = 7 - 5 + (3^2) = 5 + 9 = 14 - 8 + (4^2) = 8 + 16 = 24

Therefore, we can continue the series by adding the square of the next position to the previous term:

- 13 + (5^2) = 13 + 25 = 38 - 21 + (6^2) = 21 + 36 = 57 - 38 + (7^2) = 38 + 49 = 87

So, the next four terms of the series would be: 38, 57, 87, 126.

These are the patterns identified in the given number series, and the next four terms for each series based on those patterns.