Step-by-step explanation:
![(7 \: + \: \sqrt{6} ) ^{2}](https://tex.z-dn.net/?f=%287%20%5C%3A%20%20%2B%20%20%5C%3A%20%20%5Csqrt%7B6%7D%20%29%20%5E%7B2%7D%20)
![(7 + \sqrt{6)} (7 + \sqrt{6} )](https://tex.z-dn.net/?f=%287%20%20%2B%20%20%5Csqrt%7B6%29%7D%20%287%20%2B%20%20%5Csqrt%7B6%7D%20%29)
![49 + 14 \sqrt{6} + 6](https://tex.z-dn.net/?f=49%20%2B%2014%20%5Csqrt%7B6%7D%20%20%2B%206)
![55 + 14 \sqrt{6}](https://tex.z-dn.net/?f=55%20%2B%2014%20%5Csqrt%7B6%7D%20)
Answer:
The sequence is geometric.
![\texttt{Recursive formula, }t_n=10t_{n-1}](https://tex.z-dn.net/?f=%5Ctexttt%7BRecursive%20formula%2C%20%7Dt_n%3D10t_%7Bn-1%7D)
Step-by-step explanation:
If the sequence is arithmetic common difference will be same, if the sequence is arithmetic common ratio will be same.
Here the sequence is 4, 40, 400, 4000, …
Difference between terms
40 -4 = 36
400 - 40 = 360
They are not same , so the sequence is not arithmetic.
Ratio between terms
40/4 = 10
400/40 = 10
4000/400 = 10
They are same , so the sequence is geometric.
Now we need to find recursive formula for the sequence.
Recursive formula for GP
![t_n=rt_{n-1}](https://tex.z-dn.net/?f=t_n%3Drt_%7Bn-1%7D)
Answer:
a. (x+19)(x+1)
b. (z-1)(z-1)
c. 3(2x-3)
Step-by-step explanation:
a. x^2+20x+19
(x+19)(x+1)
b. z^2-2z+1
(z-1)(z-1)
c. 9(x-1)-3x
9x-9-3x
6x-9
3(2x-3)