Concept:1 Mark
Application: 2 Marks
Verification: 1 Mark
The 4 natural numbers which are of the form 3n + 2 (e.g 5, 8, 11, .....) are as follows:
3×1+2=3+2=5
3×2+2=6+2=8
3×3+2=9+2=11
3×4+2=12+2=14
The cubes of 5 natural numbers which are of the form 3n + 2 (e.g 5, 8, 11 .....) are as follows:
(5)3=5×5×5=125
(8)3=8×8×8=512
(11)3=11×11×11=1331
(14)3=14×14×14=2744
Verification:
125=3×41+2
512=3×170+2
1331=3×443+2
2744=3×914+2
∴ 'The cube of a natural number of the form 3n + 2 is a natural number of the same form