Q: What is the a8 term of the sequence [an] if an equals
a.) 2n - 1 ?
b.) 7?
c.) 1 + (-1)n ?
d.) – (-2)n ?
I am confused on what to do here?
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If $\displaystyle a_n = 2^{n-1} $
Then Put $\displaystyle n=8$ to get $\displaystyle n_8 = 2^{7}$
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If $\displaystyle a_n= 7$
Then the complete sequence is $\displaystyle 7 ,7, 7, 7 ,7 ,7...$
Hence $\displaystyle a_8 = 7$
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If $\displaystyle a_n= 1+(-1)^n $
Since $\displaystyle (-1)^{even~number}=1$
Thus $\displaystyle a_8=1 + {-1}^8 = 2$
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If $\displaystyle a_n = -(-2)^n $
Then $\displaystyle a_8 = - (-2)^{8} = -(-1)^8\times (2)^8 $
Thus $\displaystyle a_8 = -(2)^8$