https://file.aiquickdraw.com/mathbot/file/17265749323646omedlgb.jpg

The table in the image presents sequences with missing terms, and the goal is to complete the table for each sequence. Let's break it down term by term for each sequence to identify the patterns and complete the missing values.

### Sequence A:
1st term = 15  
2nd term = 8  
3rd term = 1  
4th term = -6

The pattern seems to decrease by 7 in each step:
- \( 15 - 7 = 8 \)
- \( 8 - 7 = 1 \)
- \( 1 - 7 = -6 \)

So, continuing this pattern:
- \( -6 - 7 = -13 \) (5th term)
- \( -13 - 7 = -20 \) (6th term)

### Sequence B:
1st term = \( \frac{5}{18} \)  
2nd term = \( \frac{6}{19} \)  
3rd term = \( \frac{7}{20} \)  
4th term = \( \frac{8}{21} \)

The pattern is that the numerator increases by 1 and the denominator increases by 1 each time:
- \( \frac{5}{18}, \frac{6}{19}, \frac{7}{20}, \frac{8}{21} \)

So, continuing this pattern:
- 5th term = \( \frac{9}{22} \)
- 6th term = \( \frac{10}{23} \)

### Sequence C:
1st term = 2  
2nd term = 5  
3rd term = 10  
4th term = 17

The pattern seems to follow a quadratic rule, where the differences between terms increase incrementally:
- \( 5 - 2 = 3 \)
- \( 10 - 5 = 5 \)
- \( 17 - 10 = 7 \)

The next difference should increase by 2:
- \( 17 + 9 = 26 \) (5th term)
- \( 26 + 11 = 37 \) (6th term)

### Sequence D:
1st term = 2  
2nd term = 6  
3rd term = 18  
4th term = 54

The pattern multiplies by 3 at each step:
- \( 2 \times 3 = 6 \)
- \( 6 \times 3 = 18 \)
- \( 18 \times 3 = 54 \)

So, continuing this pattern:
- \( 54 \times 3 = 162 \) (5th term)
- \( 162 \times 3 = 486 \) (6th term)

### Final Table (Completed):

| Sequence | 1st term | 2nd term | 3rd term | 4th term | 5th term | 6th term |


Complete the table for each sequence based on the given patterns.

This exercise involves completing sequences based on arithmetic and geometric progressions. Learn how to identify patterns in sequences and apply formulas to find the missing terms. Suitable for IGCSE Math students in Grades 9-10.

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