Define the Arithmetic Sequence:

• First term (a1): PHP 200 (the amount we save in the first week)

• Common difference (d): PHP 50 (the increase in savings each week)

The formula for the nth term of an arithmetic sequence is: an = a1 + (n-1)d Where:

a, is the amount saved in the nth week.

a₁ is the first term.

d is the common difference.

n is the number of weeks

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the "common difference" (denoted as **d**). For your scenario:

- **First term** (a₁): PHP 200 (the amount saved in the first week)
- **Common difference** (d): PHP 50 (the increase in savings each week)

The general formula for the nth term of an arithmetic sequence is given as:

\[
a_n = a_1 + (n-1) \cdot d
\]

Where:
- \(a_n\) is the amount saved in the nth week.
- \(a_1\) is the first term (PHP 200).
- \(d\) is the common difference (PHP 50).
- \(n\) is the number of weeks.

Now, let’s use this formula for a few examples:

1. **2nd week (n = 2)**:
   \[
   a_2 = 200 + (2-1) \cdot 50 = 200 + 50 = 250 \, \text{PHP}
   \]
   
2. **3rd week (n = 3)**:
   \[
   a_3 = 200 + (3-1) \cdot 50 = 200 + 100 = 300 \, \text{PHP}
   \]
   
3. **10th week (n = 10)**:
   \[
   a_{10} = 200 + (10-1) \cdot 50 = 200 + 450 = 650 \, \text{PHP}
   \]

This means the savings increase by PHP 50 each week, starting from PHP 200 in the first week.

Would you like further details or have any questions?

### Related Questions:
1. How much would you save in the 15th week?
2. What is the total amount saved after 10 weeks?
3. Can you find the sum of savings for the first 20 weeks?
4. What would the common difference be if you increased your weekly savings by PHP 100 instead?
5. If you saved PHP 1000 by the nth week, can you find n?

### Tip:
The sum of an arithmetic sequence can be easily found using the formula \( S_n = \frac{n}{2} \cdot (a_1 + a_n) \).

Define the Arithmetic Sequence: First term (a1): PHP 200 (the amount we save in the first week). Common difference (d): PHP 50 (the increase in savings each week). The formula for the nth term of an arithmetic sequence is: an = a1 + (n-1)d, where: a₁ is the first term, d is the common difference, n is the number of weeks.

Learn how to define an arithmetic sequence with the first term of PHP 200 and a common difference of PHP 50. Discover the formula for the nth term of an arithmetic sequence and calculate the savings for different weeks. Ideal for Grades 6-8.

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