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The problem you shared is about solving for terms in an arithmetic sequence (barisan aritmetika). Let's break down the problem:

### Given Information:
- The third term (\(U_3\)) of an arithmetic sequence is \(11\).
- The eighth term (\(U_8\)) is \(26\).

### Questions:
1. Find the first term (\(a\)) and the common difference (\(d\)) of the sequence.
2. Find the general formula for the \(n\)-th term (\(U_n\)).
3. Determine the 20th term (\(U_{20}\)).
4. Find the value of \(n\) such that \(U_n = 152\).

### Step-by-Step Solution:

#### 1. Finding \(a\) and \(d\)
The general formula for the \(n\)-th term of an arithmetic sequence is:
\[
U_n = a + (n-1)d
\]
For \(U_3 = 11\), we have:
\[
11 = a + (3-1)d = a + 2d
\]
For \(U_8 = 26\), we have:
\[
26 = a + (8-1)d = a + 7d
\]

Now, solve this system of equations:
\[
a + 2d = 11 \quad (1)
\]
\[
a + 7d = 26 \quad (2)
\]

Subtract equation (1) from equation (2):
\[
(a + 7d) - (a + 2d) = 26 - 11
\]
\[
5d = 15
\]
\[
d = 3
\]

Now substitute \(d = 3\) into equation (1):
\[
a + 2(3) = 11
\]
\[
a + 6 = 11
\]
\[
a = 5
\]

Thus, the first term \(a = 5\) and the common difference \(d = 3\).

#### 2. General Formula for \(U_n\)
Now that we have \(a = 5\) and \(d = 3\), the general formula for the \(n\)-th term is:
\[
U_n = 5 + (n-1)3 = 5 + 3n - 3 = 3n + 2
\]

#### 3. Finding the 20th Term
Using the general formula \(U_n = 3n + 2\), we substitute \(n = 20\):
\[
U_{20} = 3(20) + 2 = 60 + 2 = 62
\]

Thus, the 20th term is \(62\).

#### 4. Finding \(n\) such that \(U_n = 152\)
Set \(U_n = 152\) in the general formula and solve for \(n\):
\[
152 = 3n + 2
\]
\[
152 - 2 = 3n
\]
\[
150 = 3n
\]
\[
n = \frac{150}{3} = 50
\]

Thus, \(n = 50\).

### Final Answers:
1. First term (\(a\)) = 5, common difference (\(d\)) = 3.
2. General formula: \(U_n = 3n + 2\).
3. 20th term (\(U_{20}\)) = 62.
4. \(n = 50\) when \(U_n = 152\).

Would you like any more details or have further questions?

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Here are 5 related questions:
1. How do you find the sum of the first \(n\) terms of an arithmetic sequence?
2. What happens to the arithmetic sequence if the common difference is negative?
3. How would you determine if a sequence is arithmetic or geometric?
4. Can an arithmetic sequence have non-integer terms? How?
5. How do you find the common difference if you're only given non-consecutive terms?

**Tip:** In arithmetic sequences, the difference between consecutive terms is always constant, which makes it easier to identify and calculate other terms in the sequence.

Suku ketiga dalam suatu barisan aritmetika adalah 11 dan suku kedelapan adalah 26. Carilah suku pertama dan beda dari barisan aritmetika tersebut! Carilah suku ke-n! Tentukan suku ke-20! Tentukan nilai n sehingga u_n = 152!

Learn how to solve arithmetic sequence problems with a given third term of 11 and eighth term of 26. This problem covers finding the first term, common difference, general term formula, the 20th term, and determining n for a specific sequence value. Suitable for students in Grades 7-9.

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