Sequence:
[tex]\frac{1}{6},\frac{1}{12},\frac{1}{24},\frac{1}{48},\ldots[/tex]As we can see, the denominator of each term is multiplied times 2:
[tex]6\times2=12[/tex][tex]12\times2=24[/tex][tex]24\times2=48[/tex]However, this can also be written as follows:
[tex]6\times2^1=12[/tex][tex]6\times2^2=24[/tex][tex]6\times2^3=48[/tex]Thus, the formula for our sequence is:
[tex]a_n=\frac{1}{6\times2^n}[/tex]As we are asked for a15, we have to replace the values:
[tex]a_{15}=\frac{1}{6\times2^{15}}[/tex]Simplifying:
[tex]a_{15}=\frac{1}{196608}[/tex]Answer:
[tex]a_{15}=\frac{1}{196608}[/tex]