3.2.1
To find the formula for the 𝑛𝑡h term of the pattern, we need to calculate the differences between consecutive terms:
- The difference between 0 and -3 is -3
- The difference between -3 and -10 is -7
- The difference between -10 and -21 is -11
- The difference between -21 and -36 is -15
We can see that the differences are increasing by 4 each time. Therefore, the formula for the 𝑛𝑡h term can be written as 𝑛² - 3𝑛.
3.2.2
To find which term is equal to -820, we can set up the equation based on the formula we found above:
𝑛² - 3𝑛 = -820
𝑛² - 3𝑛 + 820 = 0
To solve this quadratic equation, we can use the quadratic formula:
𝑛 = [3 ± √(3² - 4 * 1 * 820)] / 2
𝑛 = [3 ± √(9 - 3280)] / 2
𝑛 = [3 ± √(-3271)] / 2
Since the square root of a negative number is not a real number, there are no real solutions for 𝑛 in this case. This means there is no term in the pattern that is equal to -820.
3.2
Given the quadratic pattern: 0, − 3, − 10, − 21, − 36...
3.2.1
Determine the formula for the 𝑛𝑡h term of the pattern.
(6)
3.2.2
Which term is equal − 820?
(5)
1 answer