The sequence -1, -8, -27, -64 consists of negative perfect cubes: specifically, -1 is (-1^3), -8 is (-2^3), -27 is (-3^3), and -64 is (-4^3). The conjecture suggests that the next term in the sequence would be (-125), which is (-5^3). Thus, the pattern follows the form of (-n^3) for (n = 1, 2, 3, 4, ...).
1, 3, 9, 27 1, 2, 4, 8, 16, 32, 64
1, 2, 4, 8, 16, 32, 64 1, 3, 9, 27, 81
-56
1³ = 1 2³ = 8 3³ = 27 4³ = 64 5³ = 125
8 x 8 = 64 32 x 2 = 64 63 + 1 = 64 100 - 36 = 64
1 8 27 64 125 ...13 23 33 43 53 63 73 ...1 8 27 64 125 216 343...
1 8 27 64 125 216 343
Cubed integers
1, 8, 27, 64, 125, 216
1, 8, 27, 64
1, 3, 9, 27 1, 2, 4, 8, 16, 32, 64
It is: 1
These are perfect cubes (of 1, 2 and 3) so the next two are 64 and 125
101
1, 8, 27, 64
1, 8, 27, 64, ...
64