Two springs of spring constant k_1 and k_2 are joined in series....

When the spring joined in series the total extension of spring is: \begin{aligned} & \Rightarrow y=y_1+y_2=\frac{-F}{k_1}-\frac{F}{k_2} \\ & \Rightarrow \quad y=-\mathrm{F}\left[\frac{1}{k_1}+\frac{1}{k_2}\right] \\ & \therefore \text{ Spring constant } k=\frac{k_1 k_2}{k_1+k_2} \end{aligned}