Write down the sequence of natural numbers leaving remainder $1$ on division by $3$ and the sequence of natural number leaving remainder $2$ on divisible by $3.$

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Solution

If the division by $3$ leads to remainder $1$ then the sequence must be in the form of $3 k + 1$ .
So, the sequence is $1, 4, 7, 10, . . . .$

If the division by $3$ leads to remainder $2$ then the sequence must be in the form of $3 k + 2$ .
So, the sequence is $2, 5, 8, 11, \dots \dots$

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Write down the sequence of natural numbers leaving remainder 1 on division by 3 and the sequence of natural number leaving remainder 2 on divisible by 3.

If the division by 3 leads to remainder 1 then the sequence must be in the form of 3k+1.So, the sequence is 1,4,7,10,....If the division by 3 leads to remainder 2 then the sequence must be in the form of 3k+2.So, the sequence is 2,5,8,11,⋯⋯

Write down the sequence of natural numbers leaving remainder $1$ on division by $3$ and the sequence of natural number leaving remainder $2$ on divisible by $3.$

If the division by $3$ leads to remainder $1$ then the sequence must be in the form of $3 k + 1$ .
So, the sequence is $1, 4, 7, 10, . . . .$

If the division by $3$ leads to remainder $2$ then the sequence must be in the form of $3 k + 2$ .
So, the sequence is $2, 5, 8, 11, \dots \dots$