High School

Find the missing terms in each of these patterns:

(a) 18, 15, 12, __, 6
(b) 102, 94, 86, __, 70, 64
(c) __, 100, 91, 82, 73
(d) 2, 4, __, 16, 32
(e) 3, 7, 11, 15, __, 19
(f) 15, 16, 18, 21, __, 30
(g) 3.5cm, 4cm, 4.5cm, 5cm, 5.5cm
(h) 5.75, 5.5, 5.25, __, 4, 4.75
(i) __, 12 1/2, 12 1/4, 12, 11 3/4

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}

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