Answer:
To represent the first five terms of sequence K by sketching a graph, you can follow these steps:
Start with the initial value, K(1) = 16, which is given.
Use the recurrence relation K(n) = K(n - 1) - n for n ≥ 2 to calculate the next terms in the sequence.
Here are the first five terms:
K(1) = 16
K(2) = K(1) - 2 = 16 - 2 = 14
K(3) = K(2) - 3 = 14 - 3 = 11
K(4) = K(3) - 4 = 11 - 4 = 7
K(5) = K(4) - 5 = 7 - 5 = 2
Now, you can sketch a graph to represent these terms. On the x-axis, you'll have the values of n (1, 2, 3, 4, 5), and on the y-axis, you'll have the corresponding values of K(n).
Here's a rough sketch of the graph:
|
16 | +
| |
| |
| |
| |
| |
| |
0|----------------+------------>
1 2 3 4 5
In the graph above, the points (1, 16), (2, 14), (3, 11), (4, 7), and (5, 2) are plotted. These points represent the first five terms of the sequence K, and you can see how the sequence decreases with each step according to the given recurrence relation.
Explanation: