How do you solve a problem that asks you to find the 500th term?
A beach ball has six vertical sections colored white, orange, yellow, blue, red, and green. If you spin the ball so that 500 colors go by and the first color is white, what is the 500th color?
How do I go about finding a formula to solve?
i think you divide 500 by 6
To solve this problem, we first need to understand the pattern of the colors on the beach ball. The given information states that the beach ball has six vertical sections colored white, orange, yellow, blue, red, and green.
Now, let's figure out how the colors repeat on the beach ball. Each complete rotation of the ball will show all six colors in order. So, after one complete rotation, we will be back to the white color.
Since there are six colors and one complete rotation brings us back to white, we can conclude that every 6th color will be white.
Next, we need to find out which color will be shown after the first color, white. We know that every sixth color is white, so the second color will be orange.
Following this pattern, we can determine the colors of subsequent terms. The third color will be yellow, the fourth color will be blue, the fifth color will be red, and the sixth color will be green.
To find the 500th color, we need to know which color corresponds to the remainder when 500 is divided by 6.
By performing the calculation 500 % 6, we get a remainder of 2.
This means that the 500th color will be the color in the second position, which is orange.
Therefore, the 500th color on the beach ball is orange.
As for finding a formula, since the pattern on the beach ball repeats every six colors, we can use modular arithmetic to find the position of any given term.
If we let n represent the term number, the color of the nth term can be found by calculating (n - 1) % 6. Here, the term numbers start from 1.
Using this formula, we can find the color for any given term number.