Show that n,n+2,n+5 is divisible by 3.

1.	Show that n,n+2,n+5 is divisible by 3.
Answer» let there be any =ve integer in form of a=bq+r where 0<=rlet b=3/..then a=3q a=3q=1and a = 3q+2case one:let n=3qn=3q{divisible by 3}n+1=3q+1{not divisible by 3}n+2=3q+2{not divisible by 3}case 2;let n= 3q+1n=3q+1{not divisible by 3}n+1=3q+1+1 =3q+2{not divisible by 3}n+2=3q+1+2 =3q+3=3[q+1]{divisible by 3}case 3:let n=3q=2n=3q+2{not divisible by 3}n+1=3q+2+1 =3q+3=3[q+1]{divisible by 3}n+2=3q+2+2 =3q+4{not divisible by 3}therefore there is only one one of the given divisible by 3 in each case....................................

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