A geometric sequence has first term $a_{1} = 64$ and common ratio $r = \dfrac{1}{2}$. What is the $14$th term?

Use the explicit formula for a geometric sequence: $a_{n} = a_{1} \cdot r^{n - 1}$. With $a_{1} = 64$, $r = 1/2$, $n = 14$: $a_{14} = 64 \cdot \left(\dfrac{1}{2}\right)^{13} = \dfrac{64}{2^{13}} = \dfrac{2^{6}}{2^{13}} = \dfrac{1}{2^{7}} = \dfrac{1}{128}$. Shortcut: $64$ already equals $2^{6}$, and multiplying by $(1/2)^{13}$ subtracts $13$ from the exponent, giving $2^{6 - 13} = 2^{-7} = 1/128$. - Trap A ($1/32 = 2^{-5}$) miscounts the exponent (uses $n$ instead of $n - 1$, or stops too early). - Traps B and D miss by a factor of $2$ in either direction.