Question

Исел ВУпражненияральныхчисла в126. Найдите закономерность, по которой составлена последовательность и дополните ее следующими двумя числами:1) 5, 6, 8, 11, 15, 20, ...;2) 2, 3, 5, 8, 13, 21, ...;3) 45, 44, 42, 39, 35, ...;4) 1, 4, 9, 16, 25, 36, 49, ...;5) 1, 8, 27, 64, 125, 216, ...;6) 2, 9, 28, 65, 126, 217, ...ьныхеслиHelp me please ​

Answer 1

ответ:

1) 5,6,8,11,15,20,26,33

2)2,3,5,8,13,21,33,50

3)45,44,42,39,35,30,24

4)1,4,9,16,25,36,49,64,81

5)1,8,27,64,125,216,313,426

6)2,9,28,65,126,217,338,489

Пошаговое объяснение:

...

Answer 2

Let's analyze each sequence one by one:

1. 5, 6, 8, 11, 15, 20, ...

To find the pattern in this sequence, we can look at the differences between consecutive terms: 6 - 5 = 1 8 - 6 = 2 11 - 8 = 3 15 - 11 = 4 20 - 15 = 5

The differences themselves form an arithmetic sequence. Each term is obtained by adding 1 to the previous difference. Therefore, the next difference should be 5 + 1 = 6. To find the next number in the original sequence, we add this difference to the last term: 20 + 6 = 26. So the next two numbers are 26 and 26.

Therefore, the completed sequence is 5, 6, 8, 11, 15, 20, 26, 26.

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

Looking at the terms in this sequence, we can observe that each term is the sum of the previous two terms:

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

So the pattern is that each term is the sum of the two preceding terms. Following this pattern, the next two terms would be 21 + 13 = 34 and 34 + 21 = 55.

Therefore, the completed sequence is 2, 3, 5, 8, 13, 21, 34, 55.

3. 45, 44, 42, 39, 35, ...

In this sequence, we can observe that each term is obtained by subtracting a decreasing number from the previous term:

45 - 1 = 44 44 - 2 = 42 42 - 3 = 39 39 - 4 = 35

So the pattern is that each term is obtained by subtracting a decreasing number from the previous term. Following this pattern, the next two terms would be 35 - 5 = 30 and 30 - 6 = 24.

Therefore, the completed sequence is 45, 44, 42, 39, 35, 30, 24.

4. 1, 4, 9, 16, 25, 36, 49, ...

In this sequence, we can observe that each term is the square of the corresponding position number:

1 = 1^2 4 = 2^2 9 = 3^2 16 = 4^2 25 = 5^2 36 = 6^2 49 = 7^2

So the pattern is that each term is the square of the corresponding position number. Following this pattern, the next two terms would be 8^2 = 64 and 9^2 = 81.

Therefore, the completed sequence is 1, 4, 9, 16, 25, 36, 49, 64, 81.

5. 1, 8, 27, 64, 125, 216, ...

Looking at the terms in this sequence, we can observe that each term is obtained by raising the position number to the power of 3:

1 = 1^3 8 = 2^3 27 = 3^3 64 = 4^3 125 = 5^3 216 = 6^3

So the pattern is that each term is obtained by raising the position number to the