Which of the following is the general term for the sequence a, -a, a, -a, . . . ?
1 answer:
Answer:
a(-1)^(n-1).
Step-by-step explanation:
This is a Geometric Sequence with common ratio r = -1.
The general term is a(-1)^(n-1).
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![\large\boxed{\sqrt[3]{3^{15}}=243}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Csqrt%5B3%5D%7B3%5E%7B15%7D%7D%3D243%7D)
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![\sqrt[3]{3^{15}}\\\\\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt[3]{3^{5\cdot3}}=\sqrt[3]{(3^5)^3}\\\\\text{use}\ \sqrt[n]{a^n}=a\\\\=3^5=243](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B3%5E%7B15%7D%7D%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20%28a%5En%29%5Em%3Da%5E%7Bnm%7D%5C%5C%5C%5C%3D%5Csqrt%5B3%5D%7B3%5E%7B5%5Ccdot3%7D%7D%3D%5Csqrt%5B3%5D%7B%283%5E5%29%5E3%7D%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20%5Csqrt%5Bn%5D%7Ba%5En%7D%3Da%5C%5C%5C%5C%3D3%5E5%3D243)