write a rule for the sequence 3,-3,-9,-15
The intervals are minus 6.
thank you
You're welcome.
To find a rule for the given sequence 3, -3, -9, -15, we can observe the pattern between consecutive terms.
If we look at the difference between each term, we can see that it decreases by 6 each time. The first difference is -3 - 3 = -6, the second difference is -9 - (-3) = -6, and the third difference is -15 - (-9) = -6.
Since the difference between consecutive terms is constant (-6), we can deduce that the rule for this sequence is a linear equation of the form y = mx + b, where y represents the term number, x represents the term, m represents the common difference, and b represents the initial term.
To find the value of m, we can consider any two consecutive terms. Let's take the first two terms (3 and -3):
m = (-3 - 3) / (2 - 1) = -6 / 1 = -6
Now that we have the value of m, we can find the value of b by substituting it into the equation using one of the terms. Let's use the first term:
3 = -6 * 1 + b
b = 3 + 6 = 9
Therefore, the rule for the given sequence is y = -6x + 9.