Answer :
Let's solve each pattern by finding the missing terms.
(a) 18, 15, 12, __, 6
This pattern shows a sequence of numbers decreasing at a constant rate. To find the rate, we can subtract any two consecutive terms:
- $18 - 15 = 3$
Since each term decreases by 3, the missing term is:
- $12 - 3 = 9$
The complete pattern is: 18, 15, 12, 9, 6
(b) 102, 94, 86, __, 70, 64
This sequence also decreases at a constant rate. Find the rate by subtracting terms:
- $102 - 94 = 8$
The sequence decreases by 8. The missing term is:
- $86 - 8 = 78$
The complete pattern is: 102, 94, 86, 78, 70, 64
(c) __, 100, 91, 82, 73
This sequence decreases by 9 (from 100 to 91, and 91 to 82):
Notice each term:
- $100 - 9 = 91$
- $91 - 9 = 82$
To find the first term, add 9 back to 100:
- $100 + 9 = 109$
The complete pattern is: 109, 100, 91, 82, 73
(d) 2, 4, __, 16, 32
Here, each term doubles. Thus, the missing term after 4 should be:
- $4 \times 2 = 8$
The complete pattern is: 2, 4, 8, 16, 32
(e) 3, 7, 11, 15, __, 19
This sequence increases by 4.
- $3 + 4 = 7$
- $7 + 4 = 11$
The missing term is:
- $15 + 4 = 19$
The complete pattern is: 3, 7, 11, 15, 19, 19
(f) 15, 16, 18, 21, __, 30
This sequence increases at a different rate:
- $15 + 1 = 16$
- $16 + 2 = 18$
- $18 + 3 = 21$
So, the next term should increase by 4:
- $21 + 4 = 25$
The complete pattern is: 15, 16, 18, 21, 25, 30
(g) 3.5\text{cm}, 4\text{cm}, 4.5\text{cm}, 5\text{cm}, 5.5\text{cm}
Notice each term increases by $0.5\text{cm}$.
- $3.5\text{cm} + 0.5\text{cm} = 4\text{cm}$
Since no term is missing, this is just verifying the pattern:
3.5cm, 4cm, 4.5cm, 5cm, 5.5cm
(h) 5.75, 5.5, 5.25, __, 4, 4.75
Here, each term decreases by 0.25:
- $5.75 - 0.25 = 5.5$
The missing term is:
- $5.25 - 0.25 = 5$
The complete pattern is: 5.75, 5.5, 5.25, 5, 4.75
(i) __, 12 \frac{1}{2}, 12 \frac{1}{4}, 12, 11 \frac{3}{4}
This sequence decreases by [tex]\frac{1}{4}[/tex] each time:
- $12 \frac{1}{2} - \frac{1}{4} = 12 \frac{1}{4}$
To find the first term, add [tex]\frac{1}{4}[/tex] to 12 [tex]\frac{1}{2}[/tex]:
- $12 \frac{1}{2} + \frac{1}{4} = 12 \frac{3}{4}$
The complete pattern is: 12 \frac{3}{4}, 12 \frac{1}{2}, 12 \frac{1}{4}, 12, 11 \frac{3}{4}