The image provided contains a word problem in Indonesian. Here’s the transcription and breakdown of the problem:

Problem Transcription (in Indonesian):

"1. Mona menabung di sebuah bank. Setiap bulan pada bulan pertama ia menabung Rp. 50.000,00. Pada bulan-bulan berikutnya, uang yang ia tabung selalu lebih besar Rp. 5.000,00 dari bulan sebelumnya. Beberapa rupiah uang yang ditabung Mona pada bulan ke-15?"

English Translation:

"1. Mona saves money in a bank. In the first month, she saves Rp 50,000.00. In the following months, the money she saves is always Rp 5,000.00 more than the previous month. How much money did Mona save in the 15th month?"

Approach to Solving:

This problem can be solved using the formula for an arithmetic sequence. The savings increase by a constant amount each month, meaning it's an arithmetic progression.

1. First month's savings (a₁): Rp 50,000.00
2. Increment each month (d): Rp 5,000.00
3. We are looking for the savings in the 15th month (a₁₅).

The formula for the $n$-th term of an arithmetic sequence is: $a_n = a_1 + (n - 1) \times d$

Substituting the values:

$a_{15} = 50,000 + (15 - 1) \times 5,000$ $a_{15} = 50,000 + 14 \times 5,000$ $a_{15} = 50,000 + 70,000 = 120,000$

So, Mona will save Rp 120,000.00 in the 15th month.

Would you like further details or have any other questions?

Here are 5 related questions to deepen understanding:

1. How much money has Mona saved by the end of the 15th month in total?
2. What is the total amount Mona saved over the first 6 months?
3. If Mona stopped saving after 12 months, what would be her total savings?
4. How many months would it take for Mona to save Rp 1,000,000.00?
5. What would be the savings in the 20th month?

Tip: Arithmetic sequences are useful for identifying patterns in problems involving regular, fixed increases (or decreases) over time.