Question

Write cubes of 5 natural numbers which are of the form 3n+1 (e.g 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 form”.


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Answer 1

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'