Question

The fourth term of an arithmetic sequence is 20. The common difference is -1/5 times the first term. Graph the sequence.

Answer 1

To graph the arithmetic sequence, we need to find the common difference and the first term. Then we can write out the sequence and plot it on a graph.

Step-by-step explanation:

To graph the arithmetic sequence, we need to find the common difference and the first term. We are given that the fourth term is 20, so we can find the common difference by subtracting the third term from the fourth term: 20 - 15 = 5.

Next, we are told that the common difference is -1/5 times the first term. Let's represent the first term as 'a'. So, the common difference is (-1/5)a.

To find 'a', we can use the information that the third term is 15. The third term can be expressed as the first term plus 2 times the common difference: 15 = a + 2(-1/5)a. Simplifying this equation gives us a = 10.5.

Now we have the first term (a = 10.5) and the common difference (-1/5 times a). We can use these values to write out the arithmetic sequence:

10.5, 10.5 - (1/5)(10.5), 10.5 - 2(1/5)(10.5), ...

Calculating the next terms gives us:

10.5, 10, 9.5, 9, 8.5, ...

These are the terms of the arithmetic sequence, and you can plot them on a graph with the term number on the x-axis and the corresponding term value on the y-axis.

Answer 2

To graph an arithmetic sequence, you can start by plotting the first few terms of the sequence on the coordinate plane. The x-axis represents the term number, and the y-axis represents the value of the term.

In this case, we are given that the fourth term is 20 and the common difference is -1/5 times the first term. Let's say the first term is x. Then, the second term is x - (1/5)x = 4/5x, the third term is 4/5x - (1/5)x = 3/5x, and the fourth term is 3/5x - (1/5)x = 2/5x.

Therefore, the first four terms of the sequence are x, 4/5x, 3/5x, and 2/5x. If we plot these terms on the coordinate plane, we get the following graph:

(0, x)

(1, 4/5x)

(2, 3/5x)

(3, 2/5x)

This graph represents the first four terms of the arithmetic sequence. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term number.

For this sequence, the fifth term is x + (-1/5)x = 4/5x. To find the sixth term, we can use the same formula: a_6 = x + (-1/5)x = 3/5x.

By continuing this process, we can plot the rest of the terms of the arithmetic sequence on the coordinate plane.

Step-by-step explanation: