Write the cubes 5 natural numbers of the from 3n+2 (i.e.5,8,11….) an

1.	Write the cubes 5 natural numbers of the from 3n+2 (i.e.5,8,11….) and verify the following:“The cube of a natural number of the form 3n+2 is a natural number of the same form i. e. when it is dividend by 3 the remainder is 2’
Answer» First 5 natural numbers in form ( 3n + 2 ) are = 5 , 8 , 11 , 14 , 17 Cubes of these numbers are, = 5³ = 5 × 5 × 5 = 125 = 8³ = 8 × 8 × 8 = 512 = 11³ = 11 × 11 × 11 = 1331 = 14³ = 14 × 14 × 14 = 2744 = 17³ = 17 × 17 × 17 = 4313 We find that all these cubes give remainder 2 when divided by 3.. Hence statement is true.

Write the cubes 5 natural numbers of the from 3n+2 (i.e.5,8,11….) and verify the following:“The cube of a natural number of the form 3n+2 is a natural number of the same form i. e. when it is dividend by 3 the remainder is 2’

Answer»

First 5 natural numbers in form ( 3n + 2 ) are = 5 , 8 , 11 , 14 , 17

Cubes of these numbers are,

= 5³ = 5 × 5 × 5 = 125

= 8³ = 8 × 8 × 8 = 512

= 11³ = 11 × 11 × 11 = 1331

= 14³ = 14 × 14 × 14 = 2744

= 17³ = 17 × 17 × 17 = 4313

We find that all these cubes give remainder 2 when divided by 3..

Hence statement is true.