Find an equation for the nth term of the sequence.

Question

-4, -16, -64, -256, ...

Answer 1

 The sequence is -4 , -16, -64, -256 .............n terms

                               =-[4 , 16 , 64 , 256 ,............n terms]

                               =-[4 , 4² , 4³ , 4⁴...........n terms]

This is a geometric mean

The first term a = 4

The ratio r = 4

The nth term of the sequence = ar^n-1

Substitute a =- 4 , r = 4 in the nth term of the sequence

                                                       = -44^n-1

                                                       = -4ⁿ.