A particle at the end of a spring executes $S.H.M$ with a period ${t_1}$. While the corresponding period for another spring is ${t_2}$. If the period of oscillation with the two springs in series is $T$ then
${T^{ - 1}} = t_1^{ - 1} + t_2^{ - 1}$
${T^2} = t_1^2 + t_2^2$
$T = {t_1} + {t_2}$
${T^{ - 2}} = t_1^{ - 2} + t_2^{ - 2}$
Solution
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