To complete the graph of the geometric sequence for a savings account that starts with $15 and increases monthly by 20%, we can calculate the first few terms of the sequence.
The first term (initial amount) is:
- \( a_1 = 15 \)
Each subsequent term can be calculated by multiplying the previous term by the common ratio, which is 1 + 0.20 = 1.20.
Calculating the first few terms:
- \( a_1 = 15 \)
- \( a_2 = 15 \times 1.20 = 18 \)
- \( a_3 = 18 \times 1.20 = 21.6 \)
- \( a_4 = 21.6 \times 1.20 = 25.92 \)
- \( a_5 = 25.92 \times 1.20 = 31.104 \)
Now, we have the following points for the graph:
- Month 1: (1, 15)
- Month 2: (2, 18)
- Month 3: (3, 21.6)
- Month 4: (4, 25.92)
- Month 5: (5, 31.104)
Graph Points
- (1, 15)
- (2, 18)
- (3, 21.6)
- (4, 25.92)
- (5, 31.104)
You can plot these points on the graph and label them accordingly. Make sure the x-axis represents the months (1 through 5), and the y-axis represents the savings account balance.