Grade 4 Number Sequences Worksheets|www.grade1to6.com - Free Printable

Let's solve each sequence step by step. These are arithmetic sequences, meaning each number increases by a constant amount.

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Problem 1: Sequence – 25, 35, 45, 55

Step 1: Find the pattern
- 35 - 25 = 10
- 45 - 35 = 10
- 55 - 45 = 10

➡️ The common difference is +10

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

The formula for the n-th term of an arithmetic sequence is:

> $$
> a_n = a + (n - 1) \times d
> $$

#### 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: Find the pattern
- 200 - 100 = 100
- 300 - 200 = 100
- 400 - 300 = 100

➡️ Common difference = +100

- First term (a) = 100
- d = 100

#### 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: Find the pattern
- 80 - 60 = 20
- 100 - 80 = 20
- 120 - 100 = 20

➡️ Common difference = +20

- a = 60
- d = 20

#### 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: Find the pattern
- 2000 - 1000 = 1000
- 3000 - 2000 = 1000
- 4000 - 3000 = 1000

➡️ Common difference = +1000

- a = 1000
- d = 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 Summary:

#### 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:

All sequences follow an arithmetic pattern where each number increases by a fixed amount. Using the formula:

> $ a_n = a + (n - 1)d $

we can find any term in the sequence without listing all numbers.

This helps students understand patterns and build skills in algebraic thinking at an early level.