Complete the Numerical Series worksheet with 10 sequences to solve.

Here are the solutions for the numerical series problems, broken down step-by-step.

1) 4, 8, 10, 20, 22, 44, 46, \_\_, \_\_, \_\_
* Pattern: The rule alternates between multiplying by 2 and adding 2.
* $4 \times 2 = 8$
* $8 + 2 = 10$
* $10 \times 2 = 20$
* $20 + 2 = 22$
* $22 \times 2 = 44$
* $44 + 2 = 46$
* Next steps:
* $46 \times 2 = \mathbf{92}$
* $92 + 2 = \mathbf{94}$
* $94 \times 2 = \mathbf{188}$

2) 1, 3, -1, -3, -7, -21, -25, \_\_, \_\_, \_\_
* Pattern: The rule alternates between multiplying by 3 and subtracting 4.
* $1 \times 3 = 3$
* $3 - 4 = -1$
* $-1 \times 3 = -3$
* $-3 - 4 = -7$
* $-7 \times 3 = -21$
* $-21 - 4 = -25$
* Next steps:
* $-25 \times 3 = \mathbf{-75}$
* $-75 - 4 = \mathbf{-79}$
* $-79 \times 3 = \mathbf{-237}$

3) 0, 1, 1, 2, 3, 5, 8, \_\_, \_\_, \_\_
* Pattern: This is the Fibonacci sequence. Each number is the sum of the two numbers before it.
* $0 + 1 = 1$
* $1 + 1 = 2$
* $1 + 2 = 3$
* $2 + 3 = 5$
* $3 + 5 = 8$
* Next steps:
* $5 + 8 = \mathbf{13}$
* $8 + 13 = \mathbf{21}$
* $13 + 21 = \mathbf{34}$

4) 4, 12, 16, 48, 52, 156, 160, \_\_, \_\_, \_\_
* Pattern: The rule alternates between multiplying by 3 and adding 4.
* $4 \times 3 = 12$
* $12 + 4 = 16$
* $16 \times 3 = 48$
* $48 + 4 = 52$
* $52 \times 3 = 156$
* $156 + 4 = 160$
* Next steps:
* $160 \times 3 = \mathbf{480}$
* $480 + 4 = \mathbf{484}$
* $484 \times 3 = \mathbf{1452}$

5) 9, 12, 7, 10, 5, 8, 3, \_\_, \_\_, \_\_
* Pattern: The rule alternates between adding 3 and subtracting 5.
* $9 + 3 = 12$
* $12 - 5 = 7$
* $7 + 3 = 10$
* $10 - 5 = 5$
* $5 + 3 = 8$
* $8 - 5 = 3$
* Next steps:
* $3 + 3 = \mathbf{6}$
* $6 - 5 = \mathbf{1}$
* $1 + 3 = \mathbf{4}$

6) 16, 22, 19, 25, 22, 28, 25, \_\_, \_\_, \_\_
* Pattern: The rule alternates between adding 6 and subtracting 3.
* $16 + 6 = 22$
* $22 - 3 = 19$
* $19 + 6 = 25$
* $25 - 3 = 22$
* $22 + 6 = 28$
* $28 - 3 = 25$
* Next steps:
* $25 + 6 = \mathbf{31}$
* $31 - 3 = \mathbf{28}$
* $28 + 6 = \mathbf{34}$

7) 4, 12, 16, 48, 52, 156, 160, \_\_, \_\_, \_\_
* Pattern: This is identical to problem #4. The rule alternates between multiplying by 3 and adding 4.
* Next steps:
* $160 \times 3 = \mathbf{480}$
* $480 + 4 = \mathbf{484}$
* $484 \times 3 = \mathbf{1452}$

8) 4, 8, 1, 2, -5, -10, -17, \_\_, \_\_, \_\_
* Pattern: The rule alternates between multiplying by 2 and subtracting 7.
* $4 \times 2 = 8$
* $8 - 7 = 1$
* $1 \times 2 = 2$
* $2 - 7 = -5$
* $-5 \times 2 = -10$
* $-10 - 7 = -17$
* Next steps:
* $-17 \times 2 = \mathbf{-34}$
* $-34 - 7 = \mathbf{-41}$
* $-41 \times 2 = \mathbf{-82}$

9) 22, 28, 21, 27, 20, 26, 19, \_\_, \_\_, \_\_
* Pattern: The rule alternates between adding 6 and subtracting 7.
* $22 + 6 = 28$
* $28 - 7 = 21$
* $21 + 6 = 27$
* $27 - 7 = 20$
* $20 + 6 = 26$
* $26 - 7 = 19$
* Next steps:
* $19 + 6 = \mathbf{25}$
* $25 - 7 = \mathbf{18}$
* $18 + 6 = \mathbf{24}$

10) 1, 2, -4, -8, -14, -28, -34, \_\_, \_\_, \_\_
* Pattern: The rule alternates between multiplying by 2 and subtracting 6.
* $1 \times 2 = 2$
* $2 - 6 = -4$
* $-4 \times 2 = -8$
* $-8 - 6 = -14$
* $-14 \times 2 = -28$
* $-28 - 6 = -34$
* Next steps:
* $-34 \times 2 = \mathbf{-68}$
* $-68 - 6 = \mathbf{-74}$
* $-74 \times 2 = \mathbf{-148}$

Final Answer:
1) 92, 94, 188
2) -75, -79, -237
3) 13, 21, 34
4) 480, 484, 1452
5) 6, 1, 4
6) 31, 28, 34
7) 480, 484, 1452
8) -34, -41, -82
9) 25, 18, 24
10) -68, -74, -148