Write the cubes of 5 natural numbers which are of the form 3n+1(eg 4,7

1.	Write the cubes of 5 natural numbers which are of the form 3n+1(eg 4,7,10,.......) and verify the following:“The cube of a natural number of the form 3n+1 is a natural number of the same from i.e. when divided by 3 it leaves the remainder 1’
Answer» First 5 natural numbers in the form of ( 3n + 1) are = 4 , 7 , 10 , 13 , 16 Cube of these numbers are, = 4³ = 4 × 4 × 4 = 64 = 7³ = 7 × 7 × 7 = 343 = 10³ = 10 × 10 × 10 = 1000 = 13³ = 13 × 13 × 13 = 2197 = 16³ = 16 × 16 × 16 = 4096 We find that all these cubes gives remainder 1 when divided by ‘3’ Hence, statement is true.

Write the cubes of 5 natural numbers which are of the form 3n+1(eg 4,7,10,.......) and verify the following:“The cube of a natural number of the form 3n+1 is a natural number of the same from i.e. when divided by 3 it leaves the remainder 1’

Answer»

First 5 natural numbers in the form of ( 3n + 1) are = 4 , 7 , 10 , 13 , 16

Cube of these numbers are,

= 4³ = 4 × 4 × 4 = 64

= 7³ = 7 × 7 × 7 = 343

= 10³ = 10 × 10 × 10 = 1000 = 13³ = 13 × 13 × 13 = 2197

= 16³ = 16 × 16 × 16 = 4096

We find that all these cubes gives remainder 1 when divided by ‘3’

Hence, statement is true.