Let's solve this step by step.

The father is distributing Rp100,000 to four children, with each younger child receiving Rp5,000 less than the next older sibling. Let the amount received by the eldest child be $x$. Then:

• The eldest receives: $x$
• The second receives: $x - 5,000$
• The third receives: $x - 10,000$
• The youngest receives: $x - 15,000$

The total amount distributed is:

$x + (x - 5,000) + (x - 10,000) + (x - 15,000) = 100,000$

Simplifying the equation:

$4x - 30,000 = 100,000$

Solving for $x$:

$4x = 130,000 \implies x = 32,500$

So, the eldest child receives Rp32,500. The youngest child receives:

$x - 15,000 = 32,500 - 15,000 = Rp17,500$

Therefore, the correct answer is:

B. Rp17,500

Would you like me to explain further or solve a similar problem? Here are some related questions:

1. How do you calculate sums of arithmetic sequences?
2. What is the formula for the sum of an arithmetic series?
3. Can you explain the concept of decreasing patterns in sequences?
4. How do you find the first term of a sequence given the sum and the difference?
5. What are real-life applications of arithmetic sequences?

Tip: Always write out equations step by step when working with sequences!