Question

Algebraic expression of sequence of natural numbers leaves remainder 1 on dividion by 3

Answer 1

First term is 1 because it leaves remainder 1 on division by 3.

Common difference is 3 because 3 is the number by which it is divided. The divisor will be the common difference.

First term - Common difference

= 1 - 3 = - 2

∴ A. E. = dn + (f - d)

= 3n - 2

Any term in the form 3n - 2 leaves remainder 1 on division by 3.

Let's check.

3 x 1 - 2 = 3 - 2 = 1

3 x 2 - 2 = 6 - 2 = 4

3 x 3 - 2 = 9 = 2 = 7

So the sequence is 1, 4, 7, 10,......

These terms leave remainder 1 on division by 3.

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