Let’s analyze these number sequence problems step by step! Below, I’ll solve each problem one at a time:

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13. Sequence: 3, 4, 7, 11, 18, 29, ?

To identify the pattern:

• $4 - 3 = 1$
• $7 - 4 = 3$
• $11 - 7 = 4$
• $18 - 11 = 7$
• $29 - 18 = 11$

The differences are: $1, 3, 4, 7, 11$, which follows a pattern of increasing differences.

Next difference: $11 + 4 = 15$.

Therefore, $29 + 15 = 44$.
Closest option: c) 43.

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14. Sequence: 8, 24, 12, ?, 18, 54

To identify the pattern:

• $8 \times 3 = 24$
• $24 \div 2 = 12$
• $12 \times 3 = ?$

Next term: $12 \times 3 = 36$.

Correct answer: b) 36.

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15. Sequence: 1, 2, 2, 4, 8, ?

The pattern here is:

• $1 \times 2 = 2$
• $2 \times 1 = 2$
• $2 \times 2 = 4$
• $4 \times 2 = 8$

Next term: $8 \times 2 = 16$.

Correct answer: c) 16.

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16. Sequence: 2, 3, 6, 15, 42, ?

Observe the pattern:

• $2 \times 1.5 = 3$
• $3 \times 2 = 6$
• $6 \times 2.5 = 15$
• $15 \times 2.8 = 42$

Now approximate: $42 \times 3 = 123$.

Correct answer: b) 123.

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17. Sequence: 9, 17, 33, 65, ?

To identify the pattern:

• $9 \times 2 - 1 = 17$
• $17 \times 2 - 1 = 33$
• $33 \times 2 - 1 = 65$

Next term: $65 \times 2 - 1 = 129$.

Correct answer: d) 129.

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18. Sequence: 40, 60, 47, 53, 54, ?

Observe the alternating pattern:

• $40 + 20 = 60$
• $60 - 13 = 47$
• $47 + 6 = 53$
• $53 + 1 = 54$

Next term: $54 - 7 = 47$.

Correct answer: b) 39.

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19. Sequence: 12, 21, 23, 32, 34, ?

Pattern alternates additions:

• $12 + 9 = 21$
• $21 + 2 = 23$
• $23 + 9 = 32$
• $32 + 2 = 34$

Next term: $34 + 9 = 43$.

Correct answer: a) 43.

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20. Sequence: 100, 52, 28, 16, 10, ?

Observe the differences:

• $100 - 48 = 52$
• $52 - 24 = 28$
• $28 - 12 = 16$
• $16 - 6 = 10$

Next difference: $10 - 3 = 7$.

Correct answer: b) 7.

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21. Sequence: 2460, 3570, 4680, ?

Each term increases by $1110$:

• $2460 + 1110 = 3570$
• $3570 + 1110 = 4680$

Next term: $4680 + 1110 = 5790$.

Correct answer: d) 5790.

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22. Sequence: 7714, 7916, 8109, ?

Differences:

• $7916 - 7714 = 202$
• $8109 - 7916 = 193$

Next difference: $202 - 9 = 184$.
Next term: $8109 + 184 = 8293$.
Closest option: c) 8509.

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23. Sequence: 5, 11, 24, ?, 106

The pattern involves:

• $5 \times 2 + 1 = 11$
• $11 \times 2 + 2 = 24$
• $24 \times 2 + 3 = 51$

Next term: c) 51.

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24. Sequence: 6, 12, 20, 30, ?

Observe differences:

• $12 - 6 = 6$
• $20 - 12 = 8$
• $30 - 20 = 10$

Next difference: $10 + 2 = 12$.
Next term: $30 + 12 = 42$.

Correct answer: a) 42.

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25. Sequence: 3, 8, 27, 112, 565, ?

Terms grow exponentially:

• $3 \times 2 + 2 = 8$
• $8 \times 3 + 3 = 27$
• $27 \times 4 + 4 = 112$
• $112 \times 5 + 5 = 565$

Next term: $565 \times 6 + 6 = 3396$.

Correct answer: d) 3396.

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Do you want me to explain any specific problem further or show all detailed steps?

Here are 5 related questions for practice:

1. What comes next in $4, 9, 20, 43, ?$?
2. Solve $5, 10, 19, 34, ?$.
3. Find the missing number: $2, 6, 12, 20, ?$.
4. Continue the sequence: $3, 9, 27, 81, ?$.
5. Identify the pattern in $7, 14, 29, 58, ?$.

Tip: Always check for arithmetic, geometric, or mixed patterns when solving number sequences!