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 f |
a |
A |
|
|
|
|
Row (f+1) |
B |
C |
|
|
|
|
- Find A in terms of a.
- Find B in terms of a.
- Find C in terms of a.
- Express a in terms of f.
(a)
A = a + 1
(b)
Pattern for Column 1
Row 1: 8 + 6 x 1 = 14
Row 2: 8 + 6 x 2 = 20
Row 3: 8 + 6 x 3 = 26
Therefore, each consecutive row differs by 6.
B = a + 6
(c)
C = a + 6 + 1 = a + 7
(d)
Pattern for Column 2
Row 1: 9 + 6 x 1 = 15
Row 2: 9 + 6 x 2 = 21
Row 3: 9 + 6 x 3 = 27
Formula: 9 + 6 x Row number
Let f be the row number
A = 9 + 6 f
a = 9 + 6f - 1 = 8 + 6f
Answer(s): (a) a + 1 or 1 + a; (b) a + 6 or 6 + a; (c) a + 7 or 7 + a; (d) 6 f + 8 or 8 + 6 f