Respuesta :
Answer:
nth term = 2n^2 - 3n - 6.
Step-by-step explanation:
n = 1 2 3 4 5 6 7
- 7 -4 3 14 29 48 71
Differences 3 7 11 15 19 23
Differences 4 4 4 4 4
So the first term in the Rule is 2n^2
Subtracting the values of 2n^2 from the original terms:
- 7 -4 3 14 29 48 71
2n^2 2 8 18 32 50 72 98
Subtrct -9 -12 -15 -18 -21 -24 -27
-3 -3 -3 -3 -3 -3
So we have -3n and the last term is -6 because -7 = 2(1)^2 -3 - 6 and the other terms fit this pattern as well.
The nth term rule of the provided quadratic sequence to find the n'th term of the sequence is 2n²-3n-6.
What is quadratic sequence?
The quadratic sequence is the series of the numbers in which the rule for the n'th term included an n squared term (n²). The quadratic equation for n can be given as,
[tex]an^2+bn+c[/tex]
Here, (2a) is equal to the second difference, (3a+b) is equal to the first difference and (a+b+c) is equal to the first term.
The sequence given in the problem is
[tex]-7, -4, 3, 14, 29, 48, 71[/tex]
Thus, (a+b+c) is,
[tex]a+b+c=-7[/tex] ......1
The first difference between the sequence is,
[tex]3,7,11,15,19,23[/tex]
Thus, the value of (3a+b) is,
[tex]3a+b=3\\b=3-3a[/tex] ......2
The second difference between the sequence is,
[tex]4,4,4,4,4[/tex]
Thus, the value of 2a is,
[tex]2a=4\\a=\dfrac{4}{2}=2[/tex]
Put this value in equation 2 as,
[tex]b=3-3\times2\\b=-3[/tex]
Put the value of a and b in equation 1 as,
[tex]2-3+c=-7\\c=-7+1\\c=-6[/tex]
Put these values in the above formula as,
[tex]2n^2-3n-6[/tex]
The nth term rule of the provided quadratic sequence to find the n'th term of the sequence is,
[tex]2n^2-3n-6[/tex]
Learn more about the quadratic sequence here;
https://brainly.com/question/26373760
