Can you give me details because i don't understand what you are asking
From the recursive rule, you have
![a_2=a_1+7](https://tex.z-dn.net/?f=a_2%3Da_1%2B7)
![a_3=a_2+7=a_1+7(2)](https://tex.z-dn.net/?f=a_3%3Da_2%2B7%3Da_1%2B7%282%29)
![a_4=a_3+7=a_1+7(3)](https://tex.z-dn.net/?f=a_4%3Da_3%2B7%3Da_1%2B7%283%29)
![a_5=a_4+7=a_1+7(4)](https://tex.z-dn.net/?f=a_5%3Da_4%2B7%3Da_1%2B7%284%29)
and so on. The general pattern for the
-th term is adding
copies of 7 to
:
![a_n=a_1+7(n-1)](https://tex.z-dn.net/?f=a_n%3Da_1%2B7%28n-1%29)
With
, the sequence is explicitly given by
![a_n=-3+7(n-1)=7n-10](https://tex.z-dn.net/?f=a_n%3D-3%2B7%28n-1%29%3D7n-10)
Answer:
![3\sqrt{13}](https://tex.z-dn.net/?f=3%5Csqrt%7B13%7D)
Step-by-step explanation:
Using the Theorem of the side of a triangle:
![x^2 = 4 * (4 + 9) = 42\\x = \sqrt{42}](https://tex.z-dn.net/?f=x%5E2%20%3D%204%20%2A%20%284%20%2B%209%29%20%3D%2042%5C%5Cx%20%3D%20%5Csqrt%7B42%7D)
And using the Height Theorem:
y = ![\sqrt{4 \cdot 9} = \sqrt{36} = 6](https://tex.z-dn.net/?f=%5Csqrt%7B4%20%5Ccdot%209%7D%20%20%3D%20%5Csqrt%7B36%7D%20%3D%206)
And by the Pythagorean Therorem:
z = ![\sqrt{6^2 + 9^2} = \sqrt{117} = 3\sqrt{13}](https://tex.z-dn.net/?f=%5Csqrt%7B6%5E2%20%2B%209%5E2%7D%20%3D%20%5Csqrt%7B117%7D%20%3D%203%5Csqrt%7B13%7D)