Find first differences for the sequence in order from a_1 to a_5. Determine whether or not the series is quadratic or not.(I used _ as a sign for a subscript)
-1, -3, -1, 5, 15
A. 2, 2, 6, 10; not quadratic
B. 2, 2, 6, 10; quadratic
C. -2, 2, 6, 10; not quadratic
D. -2, 2, 6, 10; quadratic
well, just look at the differences:
1st differences: -2 2 6 10
2nd differences: 4 4 4
Looks quadratic to me.
To find the first differences for the given sequence, we calculate the difference between consecutive terms:
-1 - (-3) = 2
-3 - (-1) = -2
-1 - (-3) = 2
5 - (-1) = 6
15 - 5 = 10
So the first differences are: 2, -2, 2, 6, 10.
To determine whether or not the series is quadratic, we need to check if the first differences form a constant second difference. If the second differences are constant, then the series can be represented by a quadratic equation.
To find the second differences, we calculate the difference between consecutive first differences:
-2 - 2 = -4
2 - (-2) = 4
6 - 2 = 4
10 - 6 = 4
Since the second differences are constant (4), the series is quadratic.
Therefore, the correct answer is D. -2, 2, 6, 10; quadratic.