Step-by-step explanation:
You already know that we use tn=an²+bn+c for these kinds of sequences:
4, 7, 14, 25, ...
- 7–4=3
- 14–7=7
now
7–3=4
So 2a=4===> a=2
![a_{1} = 4 = = > n = 1 \\ 4 = 2 \times {1}^{2} + b + c = = = = > \\ b + c = 2](https://tex.z-dn.net/?f=%20a_%7B1%7D%20%3D%204%20%3D%20%20%3D%20%20%3E%20n%20%3D%201%20%5C%5C%204%20%3D%202%20%5Ctimes%20%20%7B1%7D%5E%7B2%7D%20%20%2B%20b%20%2B%20c%20%3D%20%20%3D%20%20%3D%20%20%3D%20%20%3E%20%20%5C%5C%20b%20%2B%20c%20%3D%202)
![a_{2} = 7 = = > n = 2 = = = > \\ 7 = 2 \times {2}^{2} + 2 \times b + c = = = > \\ - 1 = 2b + c](https://tex.z-dn.net/?f=%20%20a_%7B2%7D%20%3D%207%20%3D%20%20%3D%20%20%3E%20n%20%3D%202%20%3D%20%20%3D%20%20%3D%20%20%3E%20%20%5C%5C%207%20%3D%202%20%5Ctimes%20%20%7B2%7D%5E%7B2%7D%20%20%2B%202%20%5Ctimes%20b%20%2B%20c%20%3D%20%20%3D%20%20%3D%20%20%3E%20%20%5C%5C%20%20-%201%20%3D%202b%20%2B%20c)
- b+c=2
- 2b+c=–1
b=–3, c=5
So the final result is:
![t_{n} = 2 {n}^{2} - 3n + 5](https://tex.z-dn.net/?f=%20t_%7Bn%7D%20%3D%202%20%7Bn%7D%5E%7B2%7D%20%20%20-%203n%20%2B%205)
Answer:
20
Step-by-step explanation:
The point of contact of the tangent and the diameter of the circle is a right angle.
Thus the triangle with legs 12 and 2 × 8 = 16 is right
Using Pythagoras' identity.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
?² = 12² + 16² = 144 + 256 = 400 ( take the square root of both sides )
? =
= 20
Answer:
160%
Step-by-step explanation:
45= 100%
72= ?%
100×72/45 = 160