Answer:
a(n)=n^3 where n=the nth term in the sequence and where 3=a constant exponent
PREMISES
y=Sequence 1,8,27,64,…
CALCULATIONS/OBSERVATIONS
The partial sequence 1,8,27,64,… shows a pattern where the numbers increase exponentially by powers of natural numbers beginning with 1
ALGORITHM
a(n)=n^3 where n=the nth term in the sequence and where 3=a constant exponent
PATTERN
(1) 1^3=1
(2) 2^3=8
(3) 3^3=27
(4) 4^3=64
(5) 5^3=125
(6) 6^3=216
(7) 7^3=343
(8) 8^3=512
(9) 9^3=729
(10) 10^3=1,000
(1,000) 1,000^3=1,000,000,000 (1 billion)
C.H.