To graph the six terms of the finite sequence where the first term (a1) is 5 and the common ratio (r) is 125, we first need to identify the terms of the sequence.
This sequence is geometric, which means each term is found by multiplying the previous term by the common ratio. The general formula for the nth term of a geometric sequence is given by:
an = a1 * r^(n – 1)
Now let’s calculate the first six terms:
- a1 = 5
- a2 = 5 * 125 = 625
- a3 = 625 * 125 = 78125
- a4 = 78125 * 125 = 9765625
- a5 = 9765625 * 125 = 1220703125
- a6 = 1220703125 * 125 = 152587890625
So, the six terms of the sequence are:
- a1 = 5
- a2 = 625
- a3 = 78125
- a4 = 9765625
- a5 = 1220703125
- a6 = 152587890625
To visualize these terms on a graph, you can plot each term against its position. The x-axis will represent the term number (1 through 6), and the y-axis will represent the value of each term. You’ll notice that the values increase dramatically due to the large common ratio of 125, resulting in an exponential growth curve.