Answer:
![T_n = 2n - 1 + T_{n-1}](https://tex.z-dn.net/?f=T_n%20%3D%202n%20-%201%20%2B%20T_%7Bn-1%7D)
Step-by-step explanation:
Given
![Sequence: -5,-2,3,10,19](https://tex.z-dn.net/?f=Sequence%3A%20-5%2C-2%2C3%2C10%2C19)
Required
Find the nth term
We have:
![T_1 = -5](https://tex.z-dn.net/?f=T_1%20%3D%20-5)
![T_2 = -2 = 3 - 5 = 3 + T_1](https://tex.z-dn.net/?f=T_2%20%3D%20-2%20%3D%203%20-%205%20%3D%203%20%2B%20T_1)
![T_3 = 3 = 5 - 2 = 5 + T_2](https://tex.z-dn.net/?f=T_3%20%3D%203%20%3D%205%20-%202%20%3D%205%20%2B%20T_2)
![T_4 = 10 = 7 + 3 = 7 +T_3](https://tex.z-dn.net/?f=T_4%20%3D%2010%20%3D%207%20%2B%203%20%3D%207%20%2BT_3)
![T_5 = 19 = 9 + 10 = 9 + T_4](https://tex.z-dn.net/?f=T_5%20%3D%2019%20%3D%209%20%2B%2010%20%3D%209%20%2B%20T_4)
This gives:
![T_2 = 3 + T_1 = 4 - 1 + T_1](https://tex.z-dn.net/?f=T_2%20%3D%203%20%2B%20T_1%20%3D%204%20-%201%20%2B%20T_1)
![T_3 = 5 + T_2 = 6 - 1 + T_2](https://tex.z-dn.net/?f=T_3%20%3D%205%20%2B%20T_2%20%3D%206%20-%201%20%2B%20T_2)
![T_4 = 7 +T_3 = 8 - 1 + T_3](https://tex.z-dn.net/?f=T_4%20%3D%207%20%2BT_3%20%3D%208%20-%201%20%2B%20T_3)
![T_5 = 9 + T_4 = 10 - 1 + T_4](https://tex.z-dn.net/?f=T_5%20%3D%209%20%2B%20T_4%20%3D%2010%20-%201%20%2B%20T_4)
---
Solving further, we have:
![T_2 = 4 - 1 + T_1 = 2 * 2 - 1 + T_1](https://tex.z-dn.net/?f=T_2%20%3D%204%20-%201%20%2B%20T_1%20%3D%202%20%2A%202%20-%201%20%2B%20T_1)
![T_3 = 6 - 1 + T_2 = 2 * 3 + T_2](https://tex.z-dn.net/?f=T_3%20%3D%206%20-%201%20%2B%20T_2%20%3D%202%20%2A%203%20%2B%20T_2)
![T_4 = 8 - 1 + T_3 = 2 * 4 - 1 + T_3](https://tex.z-dn.net/?f=T_4%20%3D%208%20-%201%20%2B%20T_3%20%3D%202%20%2A%204%20-%201%20%2B%20T_3)
![T_5 = 10 - 1 + T_4 = 2 * 5 - 1 + T_4](https://tex.z-dn.net/?f=T_5%20%3D%2010%20-%201%20%2B%20T_4%20%3D%202%20%2A%205%20-%201%20%2B%20T_4)
Following the above sequence: the nth term is:
![T_n = 2n - 1 + T_{n-1}](https://tex.z-dn.net/?f=T_n%20%3D%202n%20-%201%20%2B%20T_%7Bn-1%7D)
Answer:
B. ![\frac{3+\sqrt{29} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%2B%5Csqrt%7B29%7D%20%7D%7B2%7D)
Step-by-step explanation:
![\frac{-(-3)\sqrt{(-3^2-4(1)(5)} }{(2)(1)}](https://tex.z-dn.net/?f=%5Cfrac%7B-%28-3%29%5Csqrt%7B%28-3%5E2-4%281%29%285%29%7D%20%7D%7B%282%29%281%29%7D)
![=\frac{-(-3)+\sqrt{29} }{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-%28-3%29%2B%5Csqrt%7B29%7D%20%7D%7B2%7D)
Answer:x^2 +15x +36
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
The equation can be rewritten as ...
... (x -5)² + (y +3)² = 0 . . . . . . a circle of radius 0 centered at (5, -3)
This is the equation of the point (5, -3). So, ...
... x + y = 5 - 3 = 2
>> answer-1.99677419355. Estimate>> 124÷ 62 = 1 not sure