Certainly! Let's go through each sequence step-by-step to find the detailed solution.
### 6. [tex]\( 7, 14, -\frac{5}{24} \)[/tex]
To solve this problem, we need to find a pattern, common ratio, or common difference in the sequence. The first term is 7, the second term is 14, and the third term is [tex]\(-\frac{5}{24}\)[/tex].
After analyzing the terms, the result is:
[tex]\[ \text{Result} = \text{None} \][/tex]
### 8) [tex]\( 4, -i, 19, 24 \)[/tex]
Next, we analyze the sequence given: 4, [tex]\(-i\)[/tex], 19, 24. We need to check for arithmetic or geometric progression or any other pattern that might be present. However, after going through the terms and their relations, the result is:
[tex]\[ \text{Result} = \text{None} \][/tex]
### 8) [tex]\( -1, 8, 12, 16 \)[/tex]
This time, let's consider the sequence involving integer numbers: -1, 8, 12, 16.
- The first term [tex]\(a_1\)[/tex] is -1.
- The second term [tex]\(a_2\)[/tex] is 8.
- The third term [tex]\(a_3\)[/tex] is 12.
- The fourth term [tex]\(a_4\)[/tex] is 16.
Following through with this sequence, the result is:
[tex]\[ \text{Result} = \text{None} \][/tex]
### a) [tex]\( -1, 1, -1, 1, -11, -7 \)[/tex]
Finally, we examine the given sequence: [tex]\(-1, 1, -1, 1, -11, -7\)[/tex].
This sequence alternates between -1 and 1 until the last two terms, where it presents an entirely different pattern. After a proper review:
[tex]\[ \text{Result} = \text{None} \][/tex]
