The sequence described in the image is defined as:

$U_0 = 10, \quad U_{n+1} = \frac{2}{3}U_n + 1$

This is a recurrence relation. Let me know what specific calculation or explanation you'd like—finding terms, behavior as $n \to \infty$, or any other property.

Would you like:

1. The first few terms of the sequence calculated explicitly?
2. A determination of whether the sequence converges?
3. Analysis of the fixed point of the recurrence relation?
4. Graphical representation of the sequence?
5. Explanation of why the sequence converges (if it does)?

Tip: Recurrence relations like these often converge to a fixed point if the coefficient of $U_n$ is less than 1.