<h3>
Answer: 74</h3>
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Explanation:
We replace n with 54 to get
n+20 = 54+20 = 74
The 54th term is 74
So We Know That tan(x) Equals
![\tan(x) = \frac{ \sin(x) }{ \cos(x) }](https://tex.z-dn.net/?f=%20%5Ctan%28x%29%20%20%3D%20%20%5Cfrac%7B%20%5Csin%28x%29%20%7D%7B%20%5Ccos%28x%29%20%7D%20)
We Can Use Logic, We Know That Anything That Makes The Denominator 0, Will Not Work, So We Need To Know What Makes Sin(x) equal to 0 and Cos(x) equal to 1 or -1 BUT NOT 0
![\sin(0) = 0 \: \cos(0) = 1 \\ \sin(180) = 0 \: \cos(180) = - 1 \\ \sin(360) = 0 \: \cos(360) = 1 \\ \sin( - 180) = 0 \: \cos( - 180) = - 1 \\ \sin( - 360) = 0 \: \cos( - 360) = 1](https://tex.z-dn.net/?f=%20%5Csin%280%29%20%20%3D%200%20%5C%3A%20%20%5Ccos%280%29%20%20%3D%201%20%5C%5C%20%20%5Csin%28180%29%20%3D%200%20%20%5C%3A%20%20%5Ccos%28180%29%20%3D%20%20-%201%20%20%20%5C%5C%20%5Csin%28360%29%20%20%3D%200%20%5C%3A%20%20%5Ccos%28360%29%20%20%3D%201%20%5C%5C%20%20%5Csin%28%20-%20180%29%20%20%3D%200%20%5C%3A%20%20%5Ccos%28%20-%20180%29%20%20%20%3D%20%20-%201%20%5C%5C%20%5Csin%28%20-%20360%29%20%20%3D%200%20%5C%3A%20%20%20%5Ccos%28%20-%20360%29%20%20%3D%201)
![\cos(90) = 0 \\ \cos( - 90) = 0 \\ \cos(270) = 0 \\ \cos( - 270) = 0](https://tex.z-dn.net/?f=%20%5Ccos%2890%29%20%20%3D%200%20%5C%5C%20%20%5Ccos%28%20-%2090%29%20%20%3D%200%20%5C%5C%20%20%5Ccos%28270%29%20%20%3D%200%20%5C%5C%20%20%5Ccos%28%20-%20270%29%20%20%3D%200)
We Didn't Want Cosine To equal Zero Because Then We Get
![\tan(x) = \frac{ \sin(x) }{ \cos(x) } \\ \tan(x) = \frac{ \sin(90) }{ \cos(90) } \\ \tan(x) = \frac{1}{0} \\ \tan(x) = indeterminate](https://tex.z-dn.net/?f=%20%5Ctan%28x%29%20%20%3D%20%20%5Cfrac%7B%20%5Csin%28x%29%20%7D%7B%20%5Ccos%28x%29%20%7D%20%20%5C%5C%20%20%5Ctan%28x%29%20%20%3D%20%20%5Cfrac%7B%20%5Csin%2890%29%20%7D%7B%20%5Ccos%2890%29%20%7D%20%20%5C%5C%20%20%5Ctan%28x%29%20%20%3D%20%20%5Cfrac%7B1%7D%7B0%7D%20%20%5C%5C%20%20%5Ctan%28x%29%20%3D%20indeterminate)
THE ANSWER IS C : -360°,-180°,0°,180°,360°
Answer:
The function defining the sequence is;
F(n) = 2.5•3^(n-1)
Step-by-step explanation:
Here, we want to find an expression that defines explicitly what is obtained in the sequence.
Checking the sequence, we can observe that the second term is 3 multiplied by the first term, the 3rd term is 3 multiplied by the second and so on
So what this means is that, the succeeding term is 3 times the preceding term;
Also, we can see that the first term is a factor of all the numbers and this mean that;
Second term = 3 * 2.5
Third term = 9 * 2.5 = 3^2 * 2.5
Fourth term 27 * 2.5 = 3^3 * 2.5
Thus, in function form;
F(1) = 2.5•3^(1-1)
F(2) = 2.5•3^(2-1)
F(3) = 2.5•3^(3-1)
Thus;
F(n) = 2.5•3^(n-1)