1. The problem is to understand the Fibonacci sequence given by $x_1=1, x_2=1, x_3=2, x_4=3, x_5=5, x_6=8, x_7=13$. 2. The Fibonacci sequence is defined by the recurrence relation: $$x_n = x_{n-1} + x_{n-2}$$ with initial values $x_1=1$ and $x_2=1$. 3. Let's verify the given terms using the formula: - $x_3 = x_2 + x_1 = 1 + 1 = 2$ - $x_4 = x_3 + x_2 = 2 + 1 = 3$ - $x_5 = x_4 + x_3 = 3 + 2 = 5$ - $x_6 = x_5 + x_4 = 5 + 3 = 8$ - $x_7 = x_6 + x_5 = 8 + 5 = 13$ 4. Each term is the sum of the two preceding terms, which matches the given sequence. 5. This sequence appears in many natural phenomena and has important mathematical properties. Final answer: The sequence $x_n$ follows the Fibonacci rule $x_n = x_{n-1} + x_{n-2}$ with $x_1=1, x_2=1$ producing the terms $1,1,2,3,5,8,13$ as given.