How do you graph the first six terms of a finite series with initial term a1 = 3 and common ratio r = 15?

by

To graph the first six terms of a finite geometric series where the initial term a1 is 3 and the common ratio r is 15, we’ll first need to determine the terms of the series.

A finite geometric series can be defined using the formula for each term:

an = a1 * r(n-1)

In our case:

  • a1 = 3
  • r = 15

Now, we can calculate the first six terms:

  1. a1 = 3
  2. a2 = 3 * 15(2-1) = 3 * 15 = 45
  3. a3 = 3 * 15(3-1) = 3 * 152 = 3 * 225 = 675
  4. a4 = 3 * 15(4-1) = 3 * 153 = 3 * 3375 = 10125
  5. a5 = 3 * 15(5-1) = 3 * 154 = 3 * 50625 = 151875
  6. a6 = 3 * 15(6-1) = 3 * 155 = 3 * 759375 = 2278125

So, the first six terms of the series are:

  • 3
  • 45
  • 675
  • 10125
  • 151875
  • 2278125

Next, we can create a simple graph to visualize these terms. Here’s a straightforward way to create a bar graph using basic HTML:

3
45
675
10125
151875
2278125

This bar graph represents the growth of the terms in the finite series. As you can see, the values increase rapidly due to the large common ratio of 15, making the last few terms significantly higher.

Feel free to adjust the graph using CSS or a JavaScript library such as Chart.js for more advanced visuals!

Leave a Comment