Grade 3 Maths worksheet on patterns, including number sequences and real-world problems.

Problem Analysis and Solution

The image contains several number pattern problems and two word problems. Let's solve each part step by step.

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#### Number Patterns

##### Pattern 1
Numbers: \( 12, 17, 22, 27, 32, \_, \_, \_ \)

- Observation: The difference between consecutive numbers is \( 5 \).
- \( 17 - 12 = 5 \)
- \( 22 - 17 = 5 \)
- \( 27 - 22 = 5 \)
- \( 32 - 27 = 5 \)

- Continuation:
- Next number: \( 32 + 5 = 37 \)
- Next number: \( 37 + 5 = 42 \)
- Next number: \( 42 + 5 = 47 \)

- Answer: \( 37, 42, 47 \)

##### Pattern 2
Numbers: \( 3, 9, \_, \_, \_, \_ \)

- Observation: Each number is multiplied by \( 3 \) to get the next number.
- \( 3 \times 3 = 9 \)

- Continuation:
- Next number: \( 9 \times 3 = 27 \)
- Next number: \( 27 \times 3 = 81 \)
- Next number: \( 81 \times 3 = 243 \)
- Next number: \( 243 \times 3 = 729 \)

- Answer: \( 27, 81, 243, 729 \)

##### Pattern 3
Numbers: \( 10, 25, \_, \_, \_, \_ \)

- Observation: The difference between consecutive numbers increases by \( 5 \) each time.
- \( 25 - 10 = 15 \)
- Next difference: \( 15 + 5 = 20 \)
- Next difference: \( 20 + 5 = 25 \)
- Next difference: \( 25 + 5 = 30 \)
- Next difference: \( 30 + 5 = 35 \)

- Continuation:
- Next number: \( 25 + 20 = 45 \)
- Next number: \( 45 + 25 = 70 \)
- Next number: \( 70 + 30 = 100 \)
- Next number: \( 100 + 35 = 135 \)

- Answer: \( 45, 70, 100, 135 \)

##### Pattern 4
Numbers: \( 13, 20, \_, \_, \_, \_ \)

- Observation: The difference between consecutive numbers increases by \( 1 \) each time.
- \( 20 - 13 = 7 \)
- Next difference: \( 7 + 1 = 8 \)
- Next difference: \( 8 + 1 = 9 \)
- Next difference: \( 9 + 1 = 10 \)
- Next difference: \( 10 + 1 = 11 \)

- Continuation:
- Next number: \( 20 + 8 = 28 \)
- Next number: \( 28 + 9 = 37 \)
- Next number: \( 37 + 10 = 47 \)
- Next number: \( 47 + 11 = 58 \)

- Answer: \( 28, 37, 47, 58 \)

##### Pattern 5
Numbers: \( 55, 57, 59, \_, \_, \_ \)

- Observation: The difference between consecutive numbers is \( 2 \).
- \( 57 - 55 = 2 \)
- \( 59 - 57 = 2 \)

- Continuation:
- Next number: \( 59 + 2 = 61 \)
- Next number: \( 61 + 2 = 63 \)
- Next number: \( 63 + 2 = 65 \)

- Answer: \( 61, 63, 65 \)

##### Pattern 6
Numbers: \( 32, 35, \_, \_, \_, \_ \)

- Observation: The difference between consecutive numbers is \( 3 \).
- \( 35 - 32 = 3 \)

- Continuation:
- Next number: \( 35 + 3 = 38 \)
- Next number: \( 38 + 3 = 41 \)
- Next number: \( 41 + 3 = 44 \)
- Next number: \( 44 + 3 = 47 \)

- Answer: \( 38, 41, 44, 47 \)

##### Pattern 7
Numbers: \( 80, 100, \_, \_, \_ \)

- Observation: The difference between consecutive numbers is \( 20 \).
- \( 100 - 80 = 20 \)

- Continuation:
- Next number: \( 100 + 20 = 120 \)
- Next number: \( 120 + 20 = 140 \)
- Next number: \( 140 + 20 = 160 \)

- Answer: \( 120, 140, 160 \)

##### Pattern 8
Numbers: \( 25, 50, \_, \_, \_, \_ \)

- Observation: Each number is doubled to get the next number.
- \( 50 = 25 \times 2 \)

- Continuation:
- Next number: \( 50 \times 2 = 100 \)
- Next number: \( 100 \times 2 = 200 \)
- Next number: \( 200 \times 2 = 400 \)
- Next number: \( 400 \times 2 = 800 \)

- Answer: \( 100, 200, 400, 800 \)

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#### Word Problems

##### Problem 1
Arjun is picking apples in an apple orchard. He picks:
- 5 apples from the first tree,
- 15 from the second,
- 25 from the third.
If this pattern continues, how many will he pick from the 4th and 5th tree?

- Observation: The number of apples picked increases by \( 10 \) each time.
- \( 15 - 5 = 10 \)
- \( 25 - 15 = 10 \)

- Continuation:
- Apples from the 4th tree: \( 25 + 10 = 35 \)
- Apples from the 5th tree: \( 35 + 10 = 45 \)

- Answer: \( 35, 45 \)

##### Problem 2
A baker is preparing cakes for his shop. He places:
- 20 in the first tray,
- 15 in the second tray,
- 10 in the third tray.
If this pattern continues, how many will he place in the fourth and fifth tray?

- Observation: The number of cakes decreases by \( 5 \) each time.
- \( 15 - 20 = -5 \)
- \( 10 - 15 = -5 \)

- Continuation:
- Cakes in the 4th tray: \( 10 - 5 = 5 \)
- Cakes in the 5th tray: \( 5 - 5 = 0 \)

- Answer: \( 5, 0 \)

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Final Answers

1. Patterns:
- Pattern 1: \( \boxed{37, 42, 47} \)
- Pattern 2: \( \boxed{27, 81, 243, 729} \)
- Pattern 3: \( \boxed{45, 70, 100, 135} \)
- Pattern 4: \( \boxed{28, 37, 47, 58} \)
- Pattern 5: \( \boxed{61, 63, 65} \)
- Pattern 6: \( \boxed{38, 41, 44, 47} \)
- Pattern 7: \( \boxed{120, 140, 160} \)
- Pattern 8: \( \boxed{100, 200, 400, 800} \)

2. Word Problems:
- Problem 1: \( \boxed{35, 45} \)
- Problem 2: \( \boxed{5, 0} \)