Answer:
![\large\boxed{x^\frac{1}{5}=\sqrt[5]{x}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bx%5E%5Cfrac%7B1%7D%7B5%7D%3D%5Csqrt%5B5%5D%7Bx%7D%7D)
Step-by-step explanation:
![a^\frac{1}{n}=\sqrt[n]{a}\\\\\text{Therefore}\\\\x^\frac{1}{5}=\sqrt[5]{x}](https://tex.z-dn.net/?f=a%5E%5Cfrac%7B1%7D%7Bn%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5C%5C%5C%5C%5Ctext%7BTherefore%7D%5C%5C%5C%5Cx%5E%5Cfrac%7B1%7D%7B5%7D%3D%5Csqrt%5B5%5D%7Bx%7D)
The sequence is arithmetic as it goes down 3 every time
Arithmetic nth term formula is an=a1+d(n-1)
an=7-3(n-1)
an=7-3n+3
an=-3n+10
To find the 100th term substitute n for 100
a100=-3(100)+10
a100=-300+10
a100=-290
The 100th term is -290
