Math worksheet featuring number pattern exercises and sequence completion tasks.

Let's solve each part of the problem step by step and explain the reasoning clearly.

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Question 1: Find out what to add to each number to get the next one.

#### (a) 1, 3, 6, 10, ...

Let’s look at the differences between consecutive numbers:

- 3 - 1 = 2
- 6 - 3 = 3
- 10 - 6 = 4

So, we are adding increasing integers: +2, +3, +4...

Next, we should add 5 to 10:

- 10 + 5 = 15

Then:
- 15 + 6 = 21
- 21 + 7 = 28

✔ So the next numbers are: 15, 21, 28, etc.

> This is a sequence where each term increases by an incrementally increasing number (like triangular numbers).

#### (b) 0, 2, 6, 12, ...

Check the differences:

- 2 - 0 = 2
- 6 - 2 = 4
- 12 - 6 = 6

So we are adding even numbers: +2, +4, +6...

Next, add 8 to 12:

- 12 + 8 = 20

Then:
- 20 + 10 = 30
- 30 + 12 = 42

✔ So the next numbers are: 20, 30, 42, etc.

> Pattern: Each time, we're adding the next even number: +2, +4, +6, +8, ...

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Question 2: What pattern do you see in these numbers? Continue the same pattern and fill in the blanks.

#### (a) 96, 98, 100, 102, ...

Look at the differences:

- 98 - 96 = 2
- 100 - 98 = 2
- 102 - 100 = 2

➡️ The pattern is adding 2 each time → even numbers increasing by 2

So continue:

- 102 + 2 = 104
- 104 + 2 = 106
- 106 + 2 = 108

✔ Answer: 104, 106, 108

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#### (b) Write all odd numbers between 400 and 410

Odd numbers are those not divisible by 2.

List numbers from 401 to 409 (since 400 and 410 are even):

- 401 → odd ✔
- 402 → even ✘
- 403 → odd ✔
- 404 → even ✘
- 405 → odd ✔
- 406 → even ✘
- 407 → odd ✔
- 408 → even ✘
- 409 → odd ✔

✔ So odd numbers between 400 and 410 are:

401, 403, 405, 407, 409

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#### (c) Write all even numbers between 155 and 165

Even numbers are divisible by 2.

Start from the first even number after 155: 156

Then add 2 each time:

- 156
- 158
- 160
- 162
- 164

(165 is odd, so stop before it)

✔ Even numbers between 155 and 165 are:

156, 158, 160, 162, 164

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✔ Final Answers:

#### Question 1:

(a) Sequence: 1, 3, 6, 10, 15, 21, 28
→ Add 2, 3, 4, 5, 6, 7,...

(b) Sequence: 0, 2, 6, 12, 20, 30, 42
→ Add 2, 4, 6, 8, 10, 12,...

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#### Question 2:

(a) 96, 98, 100, 102, 104, 106, 108

(b) Odd numbers between 400 and 410: 401, 403, 405, 407, 409

(c) Even numbers between 155 and 165: 156, 158, 160, 162, 164

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Let me know if you'd like this explained visually or with diagrams!