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
Answers
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.