This worksheet helps students practice identifying patterns in number sequences, asking them to calculate the 10th, 20th, and 100th terms for various arithmetic progressions.

Let’s solve each sequence step by step.

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Sequence 1: 25, 35, 45, 55

This is an arithmetic sequence — each number increases by 10.

We can think of it as:
- 1st number = 25
- 2nd number = 25 + 10 = 35
- 3rd number = 25 + 10×2 = 45
- So, nth number = 25 + 10×(n - 1)

Let’s simplify that formula:
→ nth number = 25 + 10(n - 1) = 10n + 15

Check:
- n=1 → 10(1)+15 = 25 ✔
- n=2 → 10(2)+15 = 35 ✔

Now calculate:

a. Tenth number (n=10):
10×10 + 15 = 100 + 15 = 115

b. Twentieth number (n=20):
10×20 + 15 = 200 + 15 = 215

c. Hundredth number (n=100):
10×100 + 15 = 1000 + 15 = 1015

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Sequence 2: 100, 200, 300, 400

Each number increases by 100.

Formula: nth number = 100 × n

Check:
- n=1 → 100×1 = 100 ✔
- n=2 → 100×2 = 200 ✔

a. Tenth number (n=10):
100 × 10 = 1000

b. Twentieth number (n=20):
100 × 20 = 2000

c. Hundredth number (n=100):
100 × 100 = 10000

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Sequence 3: 60, 80, 100, 120

Each number increases by 20.

Formula: nth number = 60 + 20×(n - 1)

Simplify:
= 60 + 20n - 20 = 20n + 40

Check:
- n=1 → 20(1)+40 = 60 ✔
- n=2 → 20(2)+40 = 80 ✔

a. Tenth number (n=10):
20×10 + 40 = 200 + 40 = 240

b. Twentieth number (n=20):
20×20 + 40 = 400 + 40 = 440

c. Hundredth number (n=100):
20×100 + 40 = 2000 + 40 = 2040

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Sequence 4: 1000, 2000, 3000, 4000

Each number increases by 1000.

Formula: nth number = 1000 × n

Check:
- n=1 → 1000×1 = 1000 ✔
- n=2 → 1000×2 = 2000 ✔

a. Tenth number (n=10):
1000 × 10 = 10000

b. Twentieth number (n=20):
1000 × 20 = 20000

c. Hundredth number (n=100):
1000 × 100 = 100000

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Final Answer:
1a. 115
1b. 215
1c. 1015
2a. 1000
2b. 2000
2c. 10000
3a. 240
3b. 440
3c. 2040
4a. 10000
4b. 20000
4c. 100000