Respuesta :
When the difference between the two terms always changes by the common amount then the sequence is called as the quadratic sequence. The next term of the sequence 39,27,14 is 3.
Given information
The sequence given in the problem is 39,27,14.
The difference between first two terms is,
[tex]d_1=39-27\\ d_1=12[/tex]
The difference between next two terms is,
[tex]d_2=27-14\\d_2=13[/tex]
The difference between difference of the terms of the sequence is,
[tex]d=d_2-d_1\\ d=13-12\\ d=1[/tex]
Quadratic sequence
When the difference between the two terms always changes by the common amount then the sequence is called as the quadratic sequence.
Formula for nth term of the the quadratic sequence can be given as,
[tex]u_n=an^2+bn+c[/tex]
Here a is the half of the 2nd difference. Thus a is 0.5.
To find b use following formula,
[tex]3a+b=u_2-u_1\\ 3\times \dfrac{1}{2} +b=-12\\ b=-12-3\times \dfrac{1}{2} \\ b=-13.5[/tex]
To find c use the following formula.
[tex]a+b+c=36\\ 0.5-13.5+c=36\\ c=36+13\\ c=49[/tex]
To find the 4th term of the sequence, put the 4 on the place of n.
[tex]u_4=0.5\times 4^2+(-13.5)\times 4+49\\ u_4=8-54+49\\ u_4=3[/tex]
Thus the next value of the sequence 39,27,14 is 3.
Learn more about the quadratic sequence here;
https://brainly.com/question/11323348
