Let's carefully analyze each sequence to identify the patterns and determine the missing numbers.
### Step-by-Step Solution:
#### Sequence 1: [tex]\([24, 17, 19, 21, 23, 25, 27]\)[/tex]
This sequence does not have any missing elements. Let's move on to the next sequence.
#### Sequence 2: [tex]\([25, 11, 14, 17, 20, 33, 18]\)[/tex]
This sequence also does not contain any missing elements. Let's move on.
#### Sequence 3: [tex]\([26, \_, 4, 6, 9, 13, 18]\)[/tex]
Here, we notice that the second element is missing. To find it, we need to identify the pattern in the sequence.
1. The terms starting from the third term look like an arithmetic progression (4, 6, 9, 13, 18). The differences are as follows:
- [tex]\(6 - 4 = 2\)[/tex]
- [tex]\(9 - 6 = 3\)[/tex]
- [tex]\(13 - 9 = 4\)[/tex]
- [tex]\(18 - 13 = 5\)[/tex]
It appears that the difference is increasing by 1 each time.
2. To find the missing term, we need to extend the pattern backward from 4 to the missing term and then to 26.
The difference between 26 and the missing number must follow the reverse arithmetic pattern of differences:
- If the sequence incremented by [tex]\(2, 3, 4, 5\)[/tex],
- working back from 4, 6, [tex]\(9 (3), 13 (4), 18 (5)\)[/tex], we get the reverse differences [tex]\(3, 2\)[/tex]
Thus the difference pattern should keep reversing equally, backward by;
[tex]\[26 - N = 4\][/tex]
[tex]\[
N = 26 - 4
\][/tex]
Which is,
[tex]\[
N = 22
\][/tex]
So the missing term is 22.
#### Sequence 4: [tex]\([2, 19, 22, 24, 27, 24, 32]\)[/tex]
This sequence does not have any missing elements, onward.
#### Sequence 5: [tex]\([\_, -5, 3, \_, 4, 15]\)[/tex]
We notice two missing elements, one at the beginning and one at the fourth position.
1. We need to identify the pattern. Let's work with the given terms first. The terms given are:
-5, 3, 4, 15
2. Check the differences between terms:
- [tex]\(3 - (-5) = 8\)[/tex]
- [tex]\(4 - 3 = 1\)[/tex]
- [tex]\(15 - 4 = 11\)[/tex]
Now we may assume the missing terms must also be calculated keeping the identifiable coefficient distinctively the same: If pattern to be identified the incrementally.
Thus extending term before -5 upwards, reducing 8 more,
[tex]\[
-5 - 8 = -13\][/tex]
For next terms adding further
by [tex]\(4 - \)[/tex]difference,
[tex]\[4 - ( E(3-previous pattern + 4) + \][/tex]
thus,
\[ - 13 + 7 up to no filler results (- or else mapping + )27
Thus putting best fitted :
\[
7 for - observation.
Therefore, tentative recreated, should: \\ be nearer to 20
2, 7 else:
Therefore, completing
### Solution:
The two missing numbers in the sequences are:
1. Sequence 3: 22
2.Sequence 5:
\[
\-13, 7 adjusting to 20 -
]
