Question

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

Answer 1

Answer:

Step-by-step explanation:

Taking the first case, where -

Remainder = 1  (Given)

Divisor = 3  (Given)

Dividend = ?

According to the equation -

Dividend = ( Divisor × Quotient) + Remainder

On taking quotient as 1, 2, 3 and so on…

Dividend = 4, 7, 10… and so on which is an AP with   a = 4 and d = 3

Thus, the first number that leaves a remainder 1 on division with 3 is 4, therefore, the sequence of the numbers will be 4,7,10,13,16,19,22.

Taking the second case, where -

Remainder = 2  (Given)

Divisor = 3  (Given)

Dividend = ?

On taking quotient as 1,2,3 and so on..

Dividend = 5,8,11… and so on which is an AP with  a = 5 and d = 3

Thus, the first number that leaves a remainder 2 on division with 3 is 5, therefore the sequence of the numbers will be 5,8,11,14,17,20,23.