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$\\$If $a,b,c,d,e $ are in an arithmetic series then,$ \\b-a=c-b=d-c=e-d\\$Specifically,$\\b-a=e-d\Rightarrow b+d=a+e\\c-b=d-c\Rightarrow b+d=2c\\\therefore a+e=b+d=2c\\\\S_n=\frac{n}{2}[2a+(n-1)d]\\S_3=24\Rightarrow a+d=8 \ (*)\\S_6-S_3=51\Rightarrow 2a+5d=25 \ (**)\\2(*)-(**),\\2a+2d-2a-5d=16-25\Rightarrow d=3\\$Sub in $(*),\\a=5$

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