First we need to find the common ratio of the sequence. We do this by dividing each number by the previous number to it:
[tex]\frac{1}{\frac{1}{8}}=8[/tex][tex]\frac{8}{1}=8[/tex][tex]\frac{64}{8}=8[/tex]So the common ratio "r" is 8:
[tex]r=8[/tex]Now we can use the formula to find the nth term of a sequence:
[tex]a_n=a_1r^{n-1}[/tex]Where "an" is the nth term, "a1" is the first term which in this sequence is 1/8, and "r" is the common ratio which is 8. Substituting this we get the expression that can be used to find the nth term in the sequencehe sequenc:
[tex]a_n=(\frac{1}{8})(8)^{n-1}[/tex]Thus, the answer is option A: 1/8(8)^n-1
