Number patterns worksheet for students to complete sequences and identify the patterns.

Problem: Complete each sequence and describe the pattern.

Let's solve each sequence step by step and identify the pattern.

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#### Sequence 1:
183, 203, __, __, __, 283, 303

- Pattern Analysis:
- The difference between consecutive terms is constant.
- \( 203 - 183 = 20 \)
- Therefore, the sequence increases by 20 each time.

- Filling in the blanks:
- Next term after 203: \( 203 + 20 = 223 \)
- Next term after 223: \( 223 + 20 = 243 \)
- Next term after 243: \( 243 + 20 = 263 \)

- Completed Sequence:
- \( 183, 203, 223, 243, 263, 283, 303 \)

- Pattern Description:
- Add 20 to each term.

---

#### Sequence 2:
__, __, 277, 287, 297, 307, 317

- Pattern Analysis:
- The difference between consecutive terms is constant.
- \( 287 - 277 = 10 \)
- Therefore, the sequence increases by 10 each time.

- Filling in the blanks:
- Term before 277: \( 277 - 10 = 267 \)
- Term before 267: \( 267 - 10 = 257 \)

- Completed Sequence:
- \( 257, 267, 277, 287, 297, 307, 317 \)

- Pattern Description:
- Add 10 to each term.

---

#### Sequence 3:
145, 160, __, __, __, 220, 235

- Pattern Analysis:
- The difference between consecutive terms is constant.
- \( 160 - 145 = 15 \)
- Therefore, the sequence increases by 15 each time.

- Filling in the blanks:
- Next term after 160: \( 160 + 15 = 175 \)
- Next term after 175: \( 175 + 15 = 190 \)
- Next term after 190: \( 190 + 15 = 205 \)

- Completed Sequence:
- \( 145, 160, 175, 190, 205, 220, 235 \)

- Pattern Description:
- Add 15 to each term.

---

#### Sequence 4:
__, __, 307, 332, 357, 382, 407

- Pattern Analysis:
- The difference between consecutive terms is constant.
- \( 332 - 307 = 25 \)
- Therefore, the sequence increases by 25 each time.

- Filling in the blanks:
- Term before 307: \( 307 - 25 = 282 \)
- Term before 282: \( 282 - 25 = 257 \)

- Completed Sequence:
- \( 257, 282, 307, 332, 357, 382, 407 \)

- Pattern Description:
- Add 25 to each term.

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#### Sequence 5:
181, 221, __, __, __, 381, 421

- Pattern Analysis:
- The difference between consecutive terms is constant.
- \( 221 - 181 = 40 \)
- Therefore, the sequence increases by 40 each time.

- Filling in the blanks:
- Next term after 221: \( 221 + 40 = 261 \)
- Next term after 261: \( 261 + 40 = 301 \)
- Next term after 301: \( 301 + 40 = 341 \)

- Completed Sequence:
- \( 181, 221, 261, 301, 341, 381, 421 \)

- Pattern Description:
- Add 40 to each term.

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#### Sequence 6:
__, __, 280, 295, 310, 325, 340

- Pattern Analysis:
- The difference between consecutive terms is constant.
- \( 295 - 280 = 15 \)
- Therefore, the sequence increases by 15 each time.

- Filling in the blanks:
- Term before 280: \( 280 - 15 = 265 \)
- Term before 265: \( 265 - 15 = 250 \)

- Completed Sequence:
- \( 250, 265, 280, 295, 310, 325, 340 \)

- Pattern Description:
- Add 15 to each term.

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#### Sequence 7:
222, 242, __, __, __, 322, 342

- Pattern Analysis:
- The difference between consecutive terms is constant.
- \( 242 - 222 = 20 \)
- Therefore, the sequence increases by 20 each time.

- Filling in the blanks:
- Next term after 242: \( 242 + 20 = 262 \)
- Next term after 262: \( 262 + 20 = 282 \)
- Next term after 282: \( 282 + 20 = 302 \)

- Completed Sequence:
- \( 222, 242, 262, 282, 302, 322, 342 \)

- Pattern Description:
- Add 20 to each term.

---

#### Sequence 8:
__, __, 312, 342, 372, 402, 432

- Pattern Analysis:
- The difference between consecutive terms is constant.
- \( 342 - 312 = 30 \)
- Therefore, the sequence increases by 30 each time.

- Filling in the blanks:
- Term before 312: \( 312 - 30 = 282 \)
- Term before 282: \( 282 - 30 = 252 \)

- Completed Sequence:
- \( 252, 282, 312, 342, 372, 402, 432 \)

- Pattern Description:
- Add 30 to each term.

---

#### Sequence 9:
123, 173, __, __, __, 373, 423

- Pattern Analysis:
- The difference between consecutive terms is constant.
- \( 173 - 123 = 50 \)
- Therefore, the sequence increases by 50 each time.

- Filling in the blanks:
- Next term after 173: \( 173 + 50 = 223 \)
- Next term after 223: \( 223 + 50 = 273 \)
- Next term after 273: \( 273 + 50 = 323 \)

- Completed Sequence:
- \( 123, 173, 223, 273, 323, 373, 423 \)

- Pattern Description:
- Add 50 to each term.

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#### Sequence 10:
__, __, 400, 475, 550, 625, 700

- Pattern Analysis:
- The difference between consecutive terms is constant.
- \( 475 - 400 = 75 \)
- Therefore, the sequence increases by 75 each time.

- Filling in the blanks:
- Term before 400: \( 400 - 75 = 325 \)
- Term before 325: \( 325 - 75 = 250 \)

- Completed Sequence:
- \( 250, 325, 400, 475, 550, 625, 700 \)

- Pattern Description:
- Add 75 to each term.

---

#### Sequence 11:
180, 240, __, __, __, 480, 540

- Pattern Analysis:
- The difference between consecutive terms is constant.
- \( 240 - 180 = 60 \)
- Therefore, the sequence increases by 60 each time.

- Filling in the blanks:
- Next term after 240: \( 240 + 60 = 300 \)
- Next term after 300: \( 300 + 60 = 360 \)
- Next term after 360: \( 360 + 60 = 420 \)

- Completed Sequence:
- \( 180, 240, 300, 360, 420, 480, 540 \)

- Pattern Description:
- Add 60 to each term.

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#### Sequence 12:
__, __, 265, 320, 375, 430, 485

- Pattern Analysis:
- The difference between consecutive terms is constant.
- \( 320 - 265 = 55 \)
- Therefore, the sequence increases by 55 each time.

- Filling in the blanks:
- Term before 265: \( 265 - 55 = 210 \)
- Term before 210: \( 210 - 55 = 155 \)

- Completed Sequence:
- \( 155, 210, 265, 320, 375, 430, 485 \)

- Pattern Description:
- Add 55 to each term.

---

Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & 183, 203, 223, 243, 263, 283, 303 \quad \text{(Add 20)} \\
2. & 257, 267, 277, 287, 297, 307, 317 \quad \text{(Add 10)} \\
3. & 145, 160, 175, 190, 205, 220, 235 \quad \text{(Add 15)} \\
4. & 257, 282, 307, 332, 357, 382, 407 \quad \text{(Add 25)} \\
5. & 181, 221, 261, 301, 341, 381, 421 \quad \text{(Add 40)} \\
6. & 250, 265, 280, 295, 310, 325, 340 \quad \text{(Add 15)} \\
7. & 222, 242, 262, 282, 302, 322, 342 \quad \text{(Add 20)} \\
8. & 252, 282, 312, 342, 372, 402, 432 \quad \text{(Add 30)} \\
9. & 123, 173, 223, 273, 323, 373, 423 \quad \text{(Add 50)} \\
10. & 250, 325, 400, 475, 550, 625, 700 \quad \text{(Add 75)} \\
11. & 180, 240, 300, 360, 420, 480, 540 \quad \text{(Add 60)} \\
12. & 155, 210, 265, 320, 375, 430, 485 \quad \text{(Add 55)}
\end{array}
}
\]