Respuesta :
The nth term of sequence : 4,4,0,-8,-20 is -2[tex]n^{2}[/tex] + 6n .
What is nth term?
The nth term is a formula that enables us to find any term in a sequence. The ‘n‘ stands for the term number. We can make a sequence using the nth term by substituting different values for the term number(n).
According to the question
Sequence : 4,4,0,-8,-20
For nth term
we will look for pattern in it
as the difference between sequence is
4 4 0 -8 -20
FD 0 -4 -8 -12
SD -4 -4 -4
where
FD = first difference
SD = second difference
As, SD is same over here
this is a quadratic equation
The general equation of quadratic equation is
[tex]an^{2} + bn + c[/tex]
where n = number of terms
now,
1> a = SD/2
a = -4/2 = -2
2> 3a+b = FD
3 * -2 + b = 0
-6 + b = 0
b = 6
3> a + b +c = 1st term of sequence
-2 + 6 + c = 4
c = 0
Now ,substituting the value in general equation of quadratic equation is
nth term = [tex]an^{2} + bn + c[/tex]
nth term = -2[tex]n^{2}[/tex] + 6n
Hence, The nth term of sequence : 4,4,0,-8,-20 is -2[tex]n^{2}[/tex] + 6n .
To know more about nth term here:
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