Counting back by digits worksheet for practicing number sequences.

Problem Description:

The task involves filling in missing numbers in sequences that count backward by single-digit steps. Each sequence decreases by a consistent single-digit value (e.g., -1, -2, -3, etc.). We need to identify the pattern for each sequence and fill in the missing numbers accordingly.

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Solution Approach:

1. Identify the Step Size: For each sequence, determine the constant step size by which the numbers decrease.
2. Fill in Missing Numbers: Use the identified step size to calculate the missing numbers in the sequence.
3. Verify Consistency: Ensure that the sequence remains consistent with the identified step size.

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Detailed Solution for Each Sequence:

#### 1)
Sequence: `30, __, 26, 24, __, __, 18`
- Step size: The difference between 26 and 24 is -2.
- Fill in the missing numbers:
- Before 26: \(30 - 2 = 28\)
- After 24: \(24 - 2 = 22\)
- After 22: \(22 - 2 = 20\)
- Completed sequence: `30, 28, 26, 24, 22, 20, 18`

#### 2)
Sequence: `70, __, 56, __, __, 35, 28, __`
- Step size: The difference between 56 and 35 is -9, but we need to check smaller steps. The difference between 56 and 28 is -28/4 = -7 per step.
- Fill in the missing numbers:
- Before 56: \(70 - 7 = 63\)
- After 56: \(56 - 7 = 49\)
- After 49: \(49 - 7 = 42\)
- After 28: \(28 - 7 = 21\)
- Completed sequence: `70, 63, 56, 49, 42, 35, 28, 21`

#### 3)
Sequence: `__, 48, __, 40, 36, __, __, 24`
- Step size: The difference between 40 and 36 is -4.
- Fill in the missing numbers:
- Before 48: \(48 + 4 = 52\)
- After 48: \(48 - 4 = 44\)
- After 36: \(36 - 4 = 32\)
- After 32: \(32 - 4 = 28\)
- Completed sequence: `52, 48, 44, 40, 36, 32, 28, 24`

#### 4)
Sequence: `81, __, 63, 54, __, __, 27, __`
- Step size: The difference between 81 and 63 is -18/2 = -9.
- Fill in the missing numbers:
- After 81: \(81 - 9 = 72\)
- After 54: \(54 - 9 = 45\)
- After 45: \(45 - 9 = 36\)
- After 27: \(27 - 9 = 18\)
- Completed sequence: `81, 72, 63, 54, 45, 36, 27, 18`

#### 5)
Sequence: `__, 39, __, 33, 30, __, __, 21`
- Step size: The difference between 39 and 33 is -6.
- Fill in the missing numbers:
- Before 39: \(39 + 6 = 45\)
- After 39: \(39 - 6 = 33\) (already given)
- After 30: \(30 - 6 = 24\)
- After 24: \(24 - 6 = 18\)
- Completed sequence: `45, 39, 33, 33, 30, 24, 18, 21`

#### 6)
Sequence: `88, __, 72, 64, __, __, 40, __`
- Step size: The difference between 88 and 72 is -16/2 = -8.
- Fill in the missing numbers:
- After 88: \(88 - 8 = 80\)
- After 64: \(64 - 8 = 56\)
- After 56: \(56 - 8 = 48\)
- After 40: \(40 - 8 = 32\)
- Completed sequence: `88, 80, 72, 64, 56, 48, 40, 32`

#### 7)
Sequence: `__, 48, __, 36, 30, __, __, 12`
- Step size: The difference between 48 and 36 is -12/2 = -6.
- Fill in the missing numbers:
- Before 48: \(48 + 6 = 54\)
- After 48: \(48 - 6 = 42\)
- After 30: \(30 - 6 = 24\)
- After 24: \(24 - 6 = 18\)
- Completed sequence: `54, 48, 42, 36, 30, 24, 18, 12`

#### 8)
Sequence: `__, __, 55, __, __, 40, 35, __`
- Step size: The difference between 55 and 40 is -15/3 = -5.
- Fill in the missing numbers:
- Before 55: \(55 + 5 = 60\)
- Before 60: \(60 + 5 = 65\)
- After 55: \(55 - 5 = 50\)
- After 50: \(50 - 5 = 45\)
- After 35: \(35 - 5 = 30\)
- Completed sequence: `65, 60, 55, 50, 45, 40, 35, 30`

#### 9)
Sequence: `__, 72, __, __, 54, 48, __, 36`
- Step size: The difference between 72 and 54 is -18/3 = -6.
- Fill in the missing numbers:
- Before 72: \(72 + 6 = 78\)
- After 72: \(72 - 6 = 66\)
- After 66: \(66 - 6 = 60\)
- After 48: \(48 - 6 = 42\)
- Completed sequence: `78, 72, 66, 60, 54, 48, 42, 36`

#### 10)
Sequence: `84, __, 70, __, __, 49, 42, __`
- Step size: The difference between 84 and 70 is -14/2 = -7.
- Fill in the missing numbers:
- After 84: \(84 - 7 = 77\)
- After 70: \(70 - 7 = 63\)
- After 63: \(63 - 7 = 56\)
- After 42: \(42 - 7 = 35\)
- Completed sequence: `84, 77, 70, 63, 56, 49, 42, 35`

---

Final Answer:

```
1) 30, 28, 26, 24, 22, 20, 18
2) 70, 63, 56, 49, 42, 35, 28, 21
3) 52, 48, 44, 40, 36, 32, 28, 24
4) 81, 72, 63, 54, 45, 36, 27, 18
5) 45, 39, 33, 33, 30, 24, 18, 21
6) 88, 80, 72, 64, 56, 48, 40, 32
7) 54, 48, 42, 36, 30, 24, 18, 12
8) 65, 60, 55, 50, 45, 40, 35, 30
9) 78, 72, 66, 60, 54, 48, 42, 36
10) 84, 77, 70, 63, 56, 49, 42, 35
```

Boxed Answer:
\[
\boxed{
\begin{array}{l}
1) \, 30, 28, 26, 24, 22, 20, 18 \\
2) \, 70, 63, 56, 49, 42, 35, 28, 21 \\
3) \, 52, 48, 44, 40, 36, 32, 28, 24 \\
4) \, 81, 72, 63, 54, 45, 36, 27, 18 \\
5) \, 45, 39, 33, 33, 30, 24, 18, 21 \\
6) \, 88, 80, 72, 64, 56, 48, 40, 32 \\
7) \, 54, 48, 42, 36, 30, 24, 18, 12 \\
8) \, 65, 60, 55, 50, 45, 40, 35, 30 \\
9) \, 78, 72, 66, 60, 54, 48, 42, 36 \\
10) \, 84, 77, 70, 63, 56, 49, 42, 35 \\
\end{array}
}
\]