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

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

Can you help me and correct ? thank

Answer 1

1)

a (n ) = n ^ 3


1 ^ 3 = 1

2 ^ 3 = 8

3 ^ 3 = 27

4 ^ 3 = 64

5 ^ 3 = 125

6 ^ 3 = 216



2 )

a (n ) = n ^ 2 + 2 n


1 ^ 2 + 2 * 1 = 1 + 2 = 3

2 ^ 2 + 2 * 2 = 4 + 4 = 8

3 ^ 2 + 2 * 3 = 9 + 6 = 15

4 ^ 2 + 2 * 4 = 16 + 8 = 24

5 ^ 2 + 2 * 5 = 25 + 10 = 35

6 ^ 2 + 2 * 6 = 36 + 12 = 48