Provide the reaction sequences for the following conversions:
$(1)$ $1-$bromopropane from $2-$bromopropane
$(2)$ Polythene from calcium carbide

(N/A) $(1)$ Conversion of $2-$bromopropane to $1-$bromopropane:
$CH_3CHBrCH_3$ $\xrightarrow{KOH(alc.)} CH_3CH=CH_2$ $\xrightarrow{HBr, \text{peroxide}} CH_3CH_2CH_2Br$
$(2)$ Conversion of calcium carbide to polythene:
$CaC_2 + 2H_2O \rightarrow HC \equiv CH + Ca(OH)_2$
$HC \equiv CH + H_2 \xrightarrow{Pd} CH_2=CH_2$
$n(CH_2=CH_2) \xrightarrow{\text{polymerisation}} (-CH_2-CH_2-)_n$