Explanation:

Let's analyze the series step by step:

- The series is: 7, 11, 18, 29, ?, 76

- Find the pattern by checking the differences:

- 11 - 7 = 4

- 18 - 11 = 7

- 29 - 18 = 11

- Notice the differences: 4, 7, 11...

- The pattern in the differences is also increasing: 3, 4...

- 7 - 4 = 3

- 11 - 7 = 4

- Let's guess the next difference: after 11 (previous difference 4, so next one should grow by 1, i.e., +5)

- 11 + 5 = 16

- So, next term = 29 + 16 = 45

- After 16, next difference should be +6, 16 + 6 = 22

- 45 + 22 = 67

- But 76 is given at the end. So try with 47:

- 29 + 18 = 47

- 76 - 47 = 29

- Check the differences up to 47:

- 11 - 7 = 4

- 18 - 11 = 7

- 29 - 18 = 11

- 47 - 29 = 18

- 76 - 47 = 29

- Sequence of differences: 4, 7, 11, 18, 29 (Look! This matches the start of the number series itself. Each term is the sum of previous two differences, similar to Fibonacci logic.)

So the correct answer is:

- Option 1: 47