The image contains several math problems related to sequences and number patterns. We will solve the problem titled "Example 1" (例題1) which is: "According to a certain rule, numbers are arranged as follows: 1, 2, 4, 7, 11, 16,... What is the 15th number from the left?"

1. Problem Description

The image contains several math problems related to sequences and number patterns.

We will solve the problem titled "Example 1" (例題1) which is:

"According to a certain rule, numbers are arranged as follows: 1, 2, 4, 7, 11, 16,... What is the 15th number from the left?"

2. Solution Steps

The problem provides the solution. The solution indicates that the sequence is formed by adding the sequence 1, 2, 3, 4, ... to the initial number

1. So, to find the 15th number, we need to add the sum of the first 14 natural numbers to

1. The sum of the first $n$ natural numbers is given by the formula:

$S_n = \frac{n(n+1)}{2}$

In this case, $n = 14$, so the sum of the first 14 natural numbers is:

$S_{14} = \frac{14(14+1)}{2} = \frac{14 \times 15}{2} = 7 \times 15 = 105$

Therefore, the 15th number is $1 + S_{14} = 1 + 105 = 106$.

3. Final Answer

The 15th number in the sequence is 106.