Grade 4 Math worksheet on Number Sequencing, teaching students to find the tenth, twentieth, and hundredth numbers in various arithmetic sequences.

Let's solve each problem step by step.

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Problem 1: Sequence: 25, 35, 45, 55

Step 1: Identify the pattern.
- The numbers increase by 10 each time.
- 35 - 25 = 10
- 45 - 35 = 10
- 55 - 45 = 10

So, this is an arithmetic sequence with:
- First term (a) = 25
- Common difference (d) = 10

We can use the formula for the n-th term of an arithmetic sequence:
> $$
> a_n = a + (n - 1) \times d
> $$

#### a. Tenth number (n = 10):
$$
a_{10} = 25 + (10 - 1) \times 10 = 25 + 9 \times 10 = 25 + 90 = 115
$$

✔ Answer: 115

#### b. Twentieth number (n = 20):
$$
a_{20} = 25 + (20 - 1) \times 10 = 25 + 19 \times 10 = 25 + 190 = 215
$$

✔ Answer: 215

#### c. Hundredth number (n = 100):
$$
a_{100} = 25 + (100 - 1) \times 10 = 25 + 99 \times 10 = 25 + 990 = 1015
$$

✔ Answer: 1015

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Problem 2: Sequence: 100, 200, 300, 400

Step 1: Identify the pattern.
- Increases by 100 each time.
- So, common difference (d) = 100
- First term (a) = 100

Use the same formula:
> $$
> a_n = a + (n - 1) \times d
> $$

#### a. Tenth number (n = 10):
$$
a_{10} = 100 + (10 - 1) \times 100 = 100 + 9 \times 100 = 100 + 900 = 1000
$$

✔ Answer: 1000

#### b. Twentieth number (n = 20):
$$
a_{20} = 100 + (20 - 1) \times 100 = 100 + 19 \times 100 = 100 + 1900 = 2000
$$

✔ Answer: 2000

#### c. Hundredth number (n = 100):
$$
a_{100} = 100 + (100 - 1) \times 100 = 100 + 99 \times 100 = 100 + 9900 = 10000
$$

✔ Answer: 10000

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Problem 3: Sequence: 60, 80, 100, 120

Step 1: Identify the pattern.
- Increases by 20 each time.
- d = 20
- a = 60

#### a. Tenth number (n = 10):
$$
a_{10} = 60 + (10 - 1) \times 20 = 60 + 9 \times 20 = 60 + 180 = 240
$$

✔ Answer: 240

#### b. Twentieth number (n = 20):
$$
a_{20} = 60 + (20 - 1) \times 20 = 60 + 19 \times 20 = 60 + 380 = 440
$$

✔ Answer: 440

#### c. Hundredth number (n = 100):
$$
a_{100} = 60 + (100 - 1) \times 20 = 60 + 99 \times 20 = 60 + 1980 = 2040
$$

✔ Answer: 2040

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Problem 4: Sequence: 1000, 2000, 3000, 4000

Step 1: Identify the pattern.
- Increases by 1000 each time.
- d = 1000
- a = 1000

#### a. Tenth number (n = 10):
$$
a_{10} = 1000 + (10 - 1) \times 1000 = 1000 + 9 \times 1000 = 1000 + 9000 = 10000
$$

✔ Answer: 10000

#### b. Twentieth number (n = 20):
$$
a_{20} = 1000 + (20 - 1) \times 1000 = 1000 + 19 \times 1000 = 1000 + 19000 = 20000
$$

✔ Answer: 20000

#### c. Hundredth number (n = 100):
$$
a_{100} = 1000 + (100 - 1) \times 1000 = 1000 + 99 \times 1000 = 1000 + 99000 = 100000
$$

✔ Answer: 100000

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✔ Final Answers:

#### 1. Sequence: 25, 35, 45, 55
- a. 115
- b. 215
- c. 1015

#### 2. Sequence: 100, 200, 300, 400
- a. 1000
- b. 2000
- c. 10000

#### 3. Sequence: 60, 80, 100, 120
- a. 240
- b. 440
- c. 2040

#### 4. Sequence: 1000, 2000, 3000, 4000
- a. 10000
- b. 20000
- c. 100000

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🔍 Explanation Summary:

Each sequence is arithmetic, meaning it increases by a constant amount (common difference). We used the formula:
> $$
> \text{Term}_n = \text{First term} + (n - 1) \times \text{Common difference}
> $$

This helps us find any term in the sequence without listing all the numbers.

Let me know if you'd like a visual or table format!