Class IV math worksheet from Tagore International School, New Delhi, with pattern completion questions.

Problem Analysis and Solution

The worksheet contains two main sections:
1. Q1: Look at the pattern and complete the series.
2. Q2: Look at the pattern and complete the number towers.

Let's solve each part step by step.

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Q1: Look at the pattern and complete the series.

#### a) 2, 12, 22, 32, _____, _____, _____
- Pattern: The numbers increase by 10 each time.
- \( 2 + 10 = 12 \)
- \( 12 + 10 = 22 \)
- \( 22 + 10 = 32 \)
- Next: \( 32 + 10 = 42 \)
- Next: \( 42 + 10 = 52 \)
- Next: \( 52 + 10 = 62 \)

Answer: \( 42, 52, 62 \)

#### b) 26, 24, 22, 20, 18, _____, _____, _____
- Pattern: The numbers decrease by 2 each time.
- \( 26 - 2 = 24 \)
- \( 24 - 2 = 22 \)
- \( 22 - 2 = 20 \)
- \( 20 - 2 = 18 \)
- Next: \( 18 - 2 = 16 \)
- Next: \( 16 - 2 = 14 \)
- Next: \( 14 - 2 = 12 \)

Answer: \( 16, 14, 12 \)

#### c) A1, B2, C3, D4, _____, _____, _____, _____
- Pattern:
- The letters increase alphabetically (A, B, C, D, ...).
- The numbers increase sequentially (1, 2, 3, 4, ...).

- Next letter: E, next number: 5 → E5
- Next letter: F, next number: 6 → F6
- Next letter: G, next number: 7 → G7
- Next letter: H, next number: 8 → H8

Answer: \( E5, F6, G7, H8 \)

#### d) ABA, CDC, EFE, GHG, _____, _____, _____
- Pattern:
- The first and third letters are the same.
- The middle letter is the next letter in the alphabet after the first/last letter.

- ABA: A (first), B (next), A (same)
- CDC: C (first), D (next), C (same)
- EFE: E (first), F (next), E (same)
- GHG: G (first), H (next), G (same)

- Next: IJI (I, J, I)
- Next: KJK (K, L, K)
- Next: MLM (M, N, M)

Answer: \( IJI, KJK, MLM \)

#### e) 1, 2, 4, 8, _____, _____, _____
- Pattern: Each number is multiplied by 2.
- \( 1 \times 2 = 2 \)
- \( 2 \times 2 = 4 \)
- \( 4 \times 2 = 8 \)
- Next: \( 8 \times 2 = 16 \)
- Next: \( 16 \times 2 = 32 \)
- Next: \( 32 \times 2 = 64 \)

Answer: \( 16, 32, 64 \)

#### f) 5, 6, 9, 14, 21, _____, _____, _____
- Pattern: The difference between consecutive terms increases by 1 each time.
- \( 6 - 5 = 1 \)
- \( 9 - 6 = 3 \)
- \( 14 - 9 = 5 \)
- \( 21 - 14 = 7 \)
- Next difference: \( 7 + 2 = 9 \) → \( 21 + 9 = 30 \)
- Next difference: \( 9 + 2 = 11 \) → \( 30 + 11 = 41 \)
- Next difference: \( 11 + 2 = 13 \) → \( 41 + 13 = 54 \)

Answer: \( 30, 41, 54 \)

#### g) Ab2625, Cd2423, Ef2221, Gh2019, _____, _____, _____
- Pattern:
- The first two characters are alphabetical pairs (Ab, Cd, Ef, Gh, ...).
- The last four digits decrease by 20 each time.

- Ab2625 → Cd2423 (decrease by 200)
- Cd2423 → Ef2221 (decrease by 200)
- Ef2221 → Gh2019 (decrease by 200)

- Next pair: Ij, next number: \( 2019 - 200 = 1819 \) → Ij1819
- Next pair: Kl, next number: \( 1819 - 200 = 1619 \) → Kl1619
- Next pair: Mn, next number: \( 1619 - 200 = 1419 \) → Mn1419

Answer: \( Ij1819, Kl1619, Mn1419 \)

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Q2: Look at the pattern and complete the number towers.

#### a)
```
?
/ \
7 8
/ \
5 5
```
- Pattern: Each number above is the sum of the two numbers below it.
- \( 7 + 8 = 15 \)
- \( 5 + 5 = 10 \)
- Top number: \( 15 + 10 = 25 \)

Answer: \( 25 \)

#### b)
```
?
/ \
9 10 12
```
- Pattern: Each number above is the sum of the two numbers below it.
- \( 9 + 10 = 19 \)
- \( 10 + 12 = 22 \)
- Top number: \( 19 + 22 = 41 \)

Answer: \( 41 \)

#### c)
```
?
/ \
5 2
/ \
3 3
```
- Pattern: Each number above is the sum of the two numbers below it.
- \( 5 + 2 = 7 \)
- \( 3 + 3 = 6 \)
- Top number: \( 7 + 6 = 13 \)

Answer: \( 13 \)

#### d)
```
?
/ \
8 1 9
```
- Pattern: Each number above is the sum of the two numbers below it.
- \( 8 + 1 = 9 \)
- \( 1 + 9 = 10 \)
- Top number: \( 9 + 10 = 19 \)

Answer: \( 19 \)

#### e)
```
?
/ \
55 ?
/ \
75 15
```
- Pattern: Each number above is the sum of the two numbers below it.
- Bottom row: \( 75 + 15 = 90 \)
- Middle row: \( 55 + ? = 90 \)
- Solve for ?: \( ? = 90 - 55 = 35 \)
- Top number: \( 55 + 35 = 90 \)

Answer: \( 90 \)

#### f)
```
?
/ \
31 29 11
```
- Pattern: Each number above is the sum of the two numbers below it.
- \( 31 + 29 = 60 \)
- \( 29 + 11 = 40 \)
- Top number: \( 60 + 40 = 100 \)

Answer: \( 100 \)

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Final Answers:

1. Q1:
- a) \( \boxed{52, 62, 72} \)
- b) \( \boxed{16, 14, 12} \)
- c) \( \boxed{E5, F6, G7, H8} \)
- d) \( \boxed{IJI, KJK, MLM} \)
- e) \( \boxed{16, 32, 64} \)
- f) \( \boxed{30, 41, 54} \)
- g) \( \boxed{Ij1819, Kl1619, Mn1419} \)

2. Q2:
- a) \( \boxed{25} \)
- b) \( \boxed{41} \)
- c) \( \boxed{13} \)
- d) \( \boxed{19} \)
- e) \( \boxed{90} \)
- f) \( \boxed{100} \)