For Mark’s $6000, Bank Scamander offered a simple interest investment at 6% p.a.  What type of sequence does the sequence in the qeustion represent? Write down the common difference if it was an arithmetic sequence. Write down the common ratio if it was a geometric sequence.  

 

In this problem, Bank Scamander offers a simple interest investment at 6% per annum for Mark’s $6000. To understand the type of sequence represented by this situation, let's break it down:

### Simple Interest Formula:
The formula for simple interest is:

\[
I = P \times r \times t
\]
where:
- $ I $ is the interest earned,
- $ P $ is the principal (initial investment),
- $ r $ is the annual interest rate (in decimal form),
- $ t $ is the time in years.

At the end of each year, the amount of interest earned remains constant because simple interest does not compound. This is an indicator of an **arithmetic sequence**, where the same amount of interest is added each year.

### Type of Sequence:
Since the interest earned remains constant each year and increases linearly, the sequence of total amounts at the end of each year forms an **arithmetic sequence**.

### Common Difference:
For an arithmetic sequence, the common difference $ d $ is the constant amount added each year. In this case, the common difference is the interest earned each year:

\[
d = P \times r = 6000 \times 0.06 = 360
\]

So, the **common difference** is **$360**.

### Common Ratio (If it were a Geometric Sequence):
In a geometric sequence, each term is multiplied by a constant ratio. However, since simple interest doesn't involve compounding, this situation does not form a geometric sequence. But if it were geometric, the common ratio $ r $ would describe how the total amount multiplies year after year. With simple interest, the interest added each year is constant, not multiplied.

Would you like more details on how to handle geometric sequences or any further clarifications?

### 5 Related Questions:
1. How is the simple interest formula applied in more complex scenarios?
2. What is the difference between simple and compound interest?
3. How does the sequence change if the interest is compounded annually?
4. What would the total amount be after 5 years with simple interest at 6% p.a.?
5. Can you create a formula to calculate the total value after any number of years?

### Tip:
When working with sequences, always check whether the difference between terms is constant (arithmetic) or whether each term is multiplied by a constant (geometric).

For Mark’s $6000, Bank Scamander offered a simple interest investment at 6% p.a. What type of sequence does the sequence in the question represent? Write down the common difference if it was an arithmetic sequence. Write down the common ratio if it was a geometric sequence.

Discover how simple interest creates an arithmetic sequence in Mark's $6000 investment at 6% p.a. Learn the key formulas and concepts for understanding the common difference in arithmetic sequences, suitable for students in Grades 9-11.

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