The question provided involves an arithmetic sequence (barisan aritmetika), where we are given two terms:

• The 3rd term ($U_3$) is $-5$
• The 5th term ($U_5$) is $-9$

We are tasked with determining the 10th term ($U_{10}$) of the sequence.

Solution:

1. General formula for an arithmetic sequence:

   The general formula for the $n$-th term of an arithmetic sequence is:

   $U_n = a + (n - 1) \cdot d$

   where:

   • $a$ is the first term of the sequence,
   • $d$ is the common difference,
   • $n$ is the term number.

2. Write the equations for the known terms:

   Using the general formula for the 3rd and 5th terms:

   $U_3 = a + 2d = -5$ $U_5 = a + 4d = -9$

3. Solve for $a$ and $d$:

   Subtract the first equation from the second:

   $(a + 4d) - (a + 2d) = -9 - (-5)$ Simplifying:

   $2d = -4$ Therefore, the common difference is:

   $d = -2$

   Now substitute $d = -2$ into one of the original equations to find $a$. Using $U_3 = a + 2d = -5$:

   $a + 2(-2) = -5$ $a - 4 = -5$ Solving for $a$:

   $a = -1$

4. Find the 10th term:

   Now that we know $a = -1$ and $d = -2$, we can use the general formula to find the 10th term:

   $U_{10} = a + (10 - 1) \cdot d = -1 + 9(-2)$ Simplifying:

   $U_{10} = -1 - 18 = -19$

Final Answer:

The 10th term ($U_{10}$) is $-19$.

Would you like further clarification on any steps, or do you have additional questions? Here are some related questions you might consider:

1. How do we determine the common difference ($d$) in an arithmetic sequence?
2. Can the first term be directly given, and how does that affect the solution?
3. How would the solution change if this were a geometric sequence instead of an arithmetic one?
4. What other methods can be used to solve for the terms of a sequence?
5. How can the sum of the first $n$ terms of this arithmetic sequence be calculated?

Tip: In arithmetic sequences, finding two consecutive terms can always help solve for both the common difference and the first term quickly.