The image contains three math problems from Latihan 2.3, focusing on arithmetic and geometric sequences. Below are the details of the questions:

1. Find the sum of multiples of 4 between 10 and 100.

Guidance is provided to help solve the problem:

• First, write down the multiples of 4 between 10 and 100.
• The sequence starts with 12 and continues as 12, 16, 20, ..., up to 100.
• Use the arithmetic sequence formula for the $n$-th term and sum of terms: $U_n = a + (n-1) \cdot b$ where $a$ is the first term, $b$ is the common difference (in this case, 4), and $n$ is the number of terms.

2. Find the number of terms of a geometric series where the sum is 9,837.

• The formula for the sum of a geometric series is: $S_n = \frac{a(r^n - 1)}{r - 1}$ where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms.
• From the question, it looks like you need to calculate $n$ given $S_n = 9,837$.

3. A geometric series is given:

$\frac{3}{2} + 3 + 6 + 12 + \dots + Y = \frac{762}{4}$ You need to find the value of $Y$.

To solve this:

• Identify the common ratio $r$.
• Use the sum formula for a geometric series to calculate $n$, and then find $Y$.

Would you like detailed solutions for any of these problems?

Here are 5 related questions:

1. How do you calculate the sum of an arithmetic series?
2. What is the formula for the $n$-th term of an arithmetic progression?
3. How do you determine the common ratio in a geometric series?
4. What steps do you take to solve for $n$ in a geometric progression?
5. What is the difference between an arithmetic and geometric progression?

Tip: Always identify the first term and the common difference/ratio when solving sequence problems.