Question

Write cubes of 5 natural numbers of the form 3n+1(e.g. 4,7,10) and verify that the cube of

natural number of the form 3n+1 is natural number of same form.​

Answer 1

Answer:

he 5 natural number which are of the form 3n+1 (e.g 4,7,10,....) are as follows:

3×1+1=3+1=4

3×2+1=6+1=7

3×3+1=9+1=10

3×4+1=12+1=13

3×5+1=15+1=16

The cubes of 5 natural numbers which are of the form 3n+1 (e.g. 4,7,10,....) are as follows:

(4)3=4×4×4=64

(7)3=7×7×7=343

(10)3=10×10×10=1000

(13)3=13×13×13=2197

(16)3=16×16×16=4096

Verification:

64=3×21+1

343=3×114+1

1000=3×333+1

2197=3×732+1

4096=3×1365+1

∴ 'The cube of a natural number of the form 3n+

Answer 2

Answer:

The 5 natural number which are of the form 3n+1 (e.g 4,7,10,....) are as follows:

3×1+1=3+1=4

3×2+1=6+1=7

3×3+1=9+1=10

3×4+1=12+1=13

3×5+1=15+1=16

The cubes of 5 natural numbers which are of the form 3n+1 (e.g. 4,7,10,....) are as follows:

(4)³ =4×4×4=64

(7)³=7×7×7=343

(10)³=10×10×10=1000

(13)³ =13×13×13=2197

(16)³ =16×16×16=4096

Verification:

64=3×21+1

343=3×114+1

1000=3×333+1

2197=3×732+1

4096=3×1365+1

∴ 'The cube of a natural number of the form 3n+1 is a natural number of the same form'