The image you provided shows a math question that asks for the next number in a sequence:

Sequence provided: 1, 2, 3, 7, 11, 18, 29, ?

Let's analyze the pattern in this sequence to find the next number.

Observing the Differences:

• The difference between the second and first number: $2 - 1 = 1$
• The difference between the third and second number: $3 - 2 = 1$
• The difference between the fourth and third number: $7 - 3 = 4$
• The difference between the fifth and fourth number: $11 - 7 = 4$
• The difference between the sixth and fifth number: $18 - 11 = 7$
• The difference between the seventh and sixth number: $29 - 18 = 11$

Pattern in Differences:

The differences are:

• $1, 1, 4, 4, 7, 11$

Notice that the differences themselves follow a pattern where they increase by 3 every two steps:

• $1, 1$
• $4, 4$
• $7, 11$

Based on this pattern, the next difference should be $7 + 4 = 11$ (continuing the pattern).

Next Number:

Add this difference to the last number in the sequence:

• $29 + 11 = 40$

Therefore, the next number in the sequence should be 40.

Do you want more details or have any questions?

Here are 5 questions to expand on this:

1. How do different types of sequences (arithmetic, geometric, Fibonacci) differ in pattern identification?
2. Can you identify other types of sequences based on differences like quadratic or exponential patterns?
3. How would you approach solving a sequence problem with missing middle terms instead of the last term?
4. What is the significance of recognizing patterns in sequences for problem-solving in other areas of math?
5. Could this sequence have been generated by any other underlying mathematical relationship?

Tip: When analyzing number sequences, always check for both linear and non-linear patterns in the differences between consecutive terms to identify the correct pattern.