This is unclear...what is the exponent for the x and is the 1/2 on the outside also an exponent?
Sequence: 3/4, 3/16, 3/64, 3/256
a8=?
a1=3/4
a2=3/16
a3=3/64
a4=3/256
a2/a1=(3/16)/(3/4)=(3/16)*(4/3)=4/16=1/4
a3/a2=(3/64)/(3/16)=(3/64)*(16/3)=16/64=1/4
a4/a3=(3/256)/(3/64)=(3/256)*(64/3)=64/256=1/4
a2/a1=a3/a2=a4/a3=r=1/4
an=a1*r^(n-1)
an=(3/4)*(1/4)^(n-1)
an=(3/4)*(1)^(n-1)/(4)^(n-1)
an=(3/4)*(1/4^(n-1))
an=(3*1)/[4*4^(n-1)]
an=3/4^(1+n-1)
an=3/4^n
n=8→a8=3/4^8
a8=3/65,536
Answers:
The general term or nth term for the sequence is: an=3/4^n
a8=3/65,536
We are given order pairs : (2, 6), (3, 21), (4, 42), (5, 69)
The correct option is D) f(x) = 3x^2 - 6.
If we plug x=2 we get
f(2) = 3(2)^2 - 6 = 3(4) -6 = 12-6 =6. Represents (2,6)
If we plug x=3 we get
f(3) = 3(3)^2 - 6 = 3(9) -6 = 27-6 =21 Represents (4,21)
If we plug x=4 we get
f(4) = 3(4)^2 - 6 = 3(16) -6 = 48-6 =42. Represents (4,42)
If we plug x=5 we get
f(5) = 3(5)^2 - 6 = 3(25) -6 = 75-6 =69. Represents (5,69)
Therefore, D ) f(x) = 3x^2 - 6 is our correct option.
