The numbers are written in five columns to make a pattern.
| |
Column
1 |
Column
2 |
Column
3 |
Column
4 |
Column
5 |
Column
6 |
| Row 1 |
14 |
15 |
16 |
17 |
18 |
19 |
| Row 2 |
20 |
21 |
22 |
23 |
24 |
25 |
| Row 3 |
26 |
27 |
28 |
29 |
30 |
31 |
| Row 4 |
32 |
33 |
34 |
35 |
36 |
37 |
.
.
. |
|
|
|
|
|
|
| Row q |
|
|
i |
|
|
A |
| Row (q+1) |
|
|
|
|
B |
C |
- Find A in terms of q.
- Find B in terms of q.
- Find C in terms of q.
- Express k in terms of q.
(a)
A = i + 3
(b)
The number, 2 columns to the right of i = i + 2
Pattern for Column 5
Row 1 Column 5: 12 + 6 x 1 = 18
Row 2 Column 5: 12 + 6 x 2 = 24
Row 3 Column 5: 12 + 6 x 3 = 30
Therefore each consecutive row differs by 6.
B = (i + 2) + 6
B = i + 8
(c)
C = i + 8 + 1 = i + 9
(d)
Pattern for Column 3
Row 1 Column 3: 10 + 6 x 1 = 16
Row 2 Column 3: 10 + 6 x 2 = 22
Row 3 Column 3: 10 + 6 x 3 = 28
Formula:
Number = 10 + 6 x Row number
Let q be the row number
i = 10 + 6 q
Answer(s): (a) i + 3 or 3 + i ; (b) i + 8 or 8 + i ; (c) 9 + i or i + 9 ; (d) 6q + 10 or 10 + 6q or 6 q + 10 or 10 + 6 q
