Answer :
To find the missing terms in arithmetic sequences, we need to understand what an arithmetic sequence is. In an arithmetic sequence, each term is obtained by adding a fixed number, called the common difference, to the previous term.
Let's solve each part step by step:
9A: 24, 42, O, O
The common difference [tex]d[/tex] can be calculated by subtracting the first term from the second term:
[tex]d = 42 - 24 = 18[/tex]
The third term (first O) is:
[tex]24 + 18 \times 2 = 60[/tex]
The fourth term (second O) is:
[tex]24 + 18 \times 3 = 78[/tex]
9B: O, 24, 42, O
The common difference [tex]d[/tex] is:
[tex]d = 42 - 24 = 18[/tex]
The first term (O) is:
[tex]24 - 18 = 6[/tex]
The fourth term (O) is:
[tex]42 + 18 = 60[/tex]
9C: O, O, 24, 42
The common difference [tex]d[/tex] is:
[tex]d = 42 - 24 = 18[/tex]
The first term is obtained by subtracting the common difference twice from 24:
[tex]24 - 18 \times 2 = -12[/tex]
The second term is:
[tex]-12 + 18 = 6[/tex]
9D: 24, O, 42, O
The common difference [tex]d[/tex] is:
[tex]d = 42 - 24 = 18[/tex]
The second term (O) is:
[tex]24 + 18 = 42[/tex]
The fourth term (O) is:
[tex]42 + 18 = 60[/tex]
9E: O, 24, O, 42
The common difference [tex]d[/tex] is:
[tex]d = 42 - 24 = 18[/tex]
The first term (O) is:
[tex]24 - 18 = 6[/tex]
The third term (O) is:
[tex]24 + 18 = 42[/tex]
9F: 24, O, O, 42
The common difference [tex]d[/tex] is:
[tex]d = 42 - 24 = 18[/tex]
The second term (first O) is:
[tex]24 + 18 = 42[/tex]
The third term (second O) is:
[tex]42 - 18 = 24[/tex]
In each sequence, we determined the common difference and applied it to find the missing terms by following the pattern of the sequence. This is the key to solving problems involving arithmetic sequences.
