Answer: I need more information to solve for the first term.
Step-by-step explanation: To find the second difference of a quadratic sequence, we need to examine the differences between consecutive terms and then the differences between those differences.
a. To determine the second difference of the quadratic sequence:
Given:
Second term (n=2): 1
Fifth term (n=5): -14
First, let's find the differences between consecutive terms:
Difference between the second and first terms (d1): 1 - 0 = 1
Difference between the third and second terms (d2): -6 - 1 = -7
Difference between the fourth and third terms (d3): Unknown
Difference between the fifth and fourth terms (d4): -14 - Unknown
Now, let's find the differences between those differences:
Difference between d2 and d1: -7 - 1 = -8
Difference between d3 and d2: Unknown - (-7) = Unknown
Difference between d4 and d3: Unknown - Unknown = Unknown
The second difference of the quadratic sequence is -8.
b. To determine the first term of the quadratic sequence:
We know that the second difference of a quadratic sequence is a constant value. In this case, the second difference is -8.
We can use the formula for the nth term of a quadratic sequence:
Tn = an^2 + bn + c
Given:
Second term (n=2): 1
We can substitute the values into the formula:
1 = a(2)^2 + b(2) + c
1 = 4a + 2b + c