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Q57: Sequence Problem

Sequence: 3, 9, 27, 81, ?
This is a geometric progression where each term is multiplied by 3.

• $3 \times 3 = 9$
• $9 \times 3 = 27$
• $27 \times 3 = 81$
• $81 \times 3 = 243$

Answer: (d) 243

Q58: Sequence Problem

Sequence: 1, 2.1, 4.3, 7.6, 12, ?
The differences between consecutive terms are increasing:

• $2.1 - 1 = 1.1$
• $4.3 - 2.1 = 2.2$
• $7.6 - 4.3 = 3.3$
• $12 - 7.6 = 4.4$

The next difference should be $5.5$:

• $12 + 5.5 = 17.5$

Answer: (c) 17.5

Q59: Sequence Problem

Sequence: 196, 169, 144, 121, 100, 81, ?
This sequence involves consecutive square numbers:

• $14^2 = 196$
• $13^2 = 169$
• $12^2 = 144$
• $11^2 = 121$
• $10^2 = 100$
• $9^2 = 81$
• $8^2 = 64$

Answer: (d) 64

Q60: Sequence Problem

Sequence: 5, 9, 15, 23, __, 45
Find the differences between consecutive terms:

• $9 - 5 = 4$
• $15 - 9 = 6$
• $23 - 15 = 8$

The next difference is $10$:

• $23 + 10 = 33$

Answer: (a) 33

Q61: Sequence Problem

Sequence: 0.4, 0.8, 1.3, 1.9, __
Find the differences between consecutive terms:

• $0.8 - 0.4 = 0.4$
• $1.3 - 0.8 = 0.5$
• $1.9 - 1.3 = 0.6$

The next difference is $0.7$:

• $1.9 + 0.7 = 2.6$

Answer: (b) 2.6

Q62: Sequence Problem

Sequence: 2.7, 2.4, 2.1, 1.8, __
Find the differences between consecutive terms:

• $2.7 - 2.4 = 0.3$
• $2.4 - 2.1 = 0.3$
• $2.1 - 1.8 = 0.3$

The next term is $1.8 - 0.3 = 1.5$.

Answer: (b) 1.5

Q63: Sequence Problem

Sequence: 2, 4, 12, 48, 240, __
This is a geometric progression with varying multipliers:

• $2 \times 2 = 4$
• $4 \times 3 = 12$
• $12 \times 4 = 48$
• $48 \times 5 = 240$

The next term is $240 \times 6 = 1440$.

Answer: (b) 1440

Q64: Sequence Problem

Sequence: 125, 80, 45, 20, __
Find the differences between consecutive terms:

• $125 - 80 = 45$
• $80 - 45 = 35$
• $45 - 20 = 25$

The next difference is $15$:

• $20 - 15 = 5$.

Answer: (a) 5

Q65: Sequence Problem

Sequence: 41, 43, 47, 53, 61, __
These are consecutive prime numbers:

• $41, 43, 47, 53, 61$
  The next prime number is $67$.

Answer: (c) 67

Let me know if you'd like detailed explanations for any question or further clarifications!

Follow-up Questions:

1. How do we identify arithmetic vs. geometric sequences?
2. What are prime numbers, and how are they used in sequences?
3. Can you explain other types of progressions (like harmonic progressions)?
4. How to predict the next term when the sequence is not obvious?
5. Are there mathematical tricks to solve these sequences faster?

Tip:

Always look for patterns like differences, ratios, or squares in sequences—they often reveal the logic behind the progression!