Question

Write the next term of sequence,and then write the rule for the nth term.

1)1,8,27,64,....125
the nth is n

2) 3,8,15, 24,.....35
the nth is

Can you help me and correct ? thank you

Answer 1

1) looks like you are dealing with the cubes
so term(n) = n^3

2) did you notice that each term is one less than a perfect square?
e.g.
3 = 2^2 - 1 --term(1)
8 = 3^2 -1 -- term(2)
15 = 4^2 -1
24 = 5^2 - 1
35 = 6^2 - 1

so term(n) = (n+1)^2 -1