. Adam saved RM16500 in 10 years. In each year after the first he saved RM100 more than
he did in the preceding year. How much did he save in the first year?

Let's denote the amount Adam saved in the first year as \( a \). According to the problem, in each subsequent year, he saved RM100 more than the previous year. This means the amount saved in the second year is \( a + 100 \), in the third year it’s \( a + 200 \), and so on.

The total amount Adam saved over 10 years can be represented as the sum of an arithmetic series:

\[
S_n = \frac{n}{2} \times (2a + (n-1)d)
\]

Where:
- \( S_n \) is the total savings,
- \( n \) is the number of years (10 years),
- \( a \) is the amount saved in the first year,
- \( d \) is the common difference between the amounts saved each year (RM100).

Plugging in the values:

\[
16500 = \frac{10}{2} \times (2a + (10-1) \times 100)
\]

Simplifying this:

\[
16500 = 5 \times (2a + 900)
\]

\[
16500 = 10a + 4500
\]

Subtracting 4500 from both sides:

\[
12000 = 10a
\]

Dividing by 10:

\[
a = 1200
\]

So, Adam saved **RM1200** in the first year.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How do you find the sum of an arithmetic series?
2. What would happen if the common difference was negative?
3. Can this method be used to calculate savings over different time periods?
4. How much did Adam save in the final (10th) year?
5. What if Adam saved RM100 less each year instead?

**Tip:** Arithmetic sequences are common in financial calculations, like savings plans or loan payments, making it useful to understand them well.

Learn how to calculate Adam's savings over 10 years, starting with an initial amount and increasing savings each subsequent year. This problem involves the sum of an arithmetic series formula and is suitable for high school students.

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