To solve this problem, we need to analyze the given information in the context of an arithmetic sequence.

The problem states:

• The sum of the first term (suku ke-1) and the third term (suku ke-3) is 30.
• The sum of the logarithms of the first, second, and third terms is $3 + \log 3$.

Let's define the first term of the arithmetic sequence as $a$, and the common difference as $d$. Then:

• The first term is $a$.
• The second term is $a + d$.
• The third term is $a + 2d$.

From the first piece of information: $a + (a + 2d) = 30$ $2a + 2d = 30$ $a + d = 15 \quad \text{(Equation 1)}$

From the second piece of information (sum of the logarithms): $\log(a) + \log(a + d) + \log(a + 2d) = 3 + \log 3$ Using the property $\log x + \log y = \log(xy)$, this becomes: $\log(a(a + d)(a + 2d)) = 3 + \log 3$ This simplifies to: $\log(a(a + d)(a + 2d)) = \log(1000 \times 3) = \log(3000)$ Thus, we have: $a(a + d)(a + 2d) = 3000 \quad \text{(Equation 2)}$

Now, using Equation 1, $a + d = 15$, we substitute into Equation 2 and solve for the possible values of $a$ and $d$.

Let me now calculate the values that satisfy these conditions. sympy import symbols, Eq, solve, log

Define the variables

a, d = symbols('a d')

Equation 1: a + d = 15

eq1 = Eq(a + d, 15)

Equation 2: a(a + d)(a + 2d) = 3000

eq2 = Eq(a * (a + d) * (a + 2 * d), 3000)

Solve the system of equations

solution = solve((eq1, eq2), (a, d)) solutionThe solution to the system of equations gives two possible pairs for the values of $a$ and $d$:

1. $a = 10$, $d = 5$
2. $a = 20$, $d = -5$

Thus, the first term (suku ke-1) could either be 10 or 20, depending on the value of the common difference.

Looking at the choices in the question, the correct answer is:

• D. 10 atau 20

Would you like further clarification on this or more detailed steps? Feel free to ask!

Here are some related questions:

1. What is the general formula for the $n$-th term in an arithmetic sequence?
2. How do you calculate the sum of an arithmetic sequence?
3. How do logarithmic properties help in solving equations with multiple terms?
4. What happens if the common difference in an arithmetic sequence is negative?
5. How can we extend this problem to an infinite arithmetic sequence?

Tip: In problems involving logarithms, remember to use the properties of logarithms like the product rule $\log(ab) = \log(a) + \log(b)$ to simplify expressions.