等差数列 $\left\{a_{n}\right\}$ 中, $S_{10}=4 S_{5}$, 则 $\frac{a_{1}}{d}$ 等于 $(\quad)$
解析 由题意得:

$10 a_{1}+\frac{1}{2} \times 10 \times 9 d=4\left(5 a_{1}+\frac{1}{2} \times 5 \times 4 d\right)$,

$\therefore 10 a_{1}+45 d=20 a_{1}+40 d$,

$\therefore 10 a_{1}=5 d, \quad \therefore \frac{a_{1}}{d}=\frac{1}{2}$.