Question

What is the explicit formula of the geometric sequence?2, -8, 32, -128,...

Answer 1

EXPLANATION

Geometric Progression:

A geometric sequence has a constant ratio r and is defined by:

`a_n=a_0\cdot r^(n-1)`

Check wheter the ratio is constant: r=-4

2, -8 , 32, -128

Compute the ratios of all the adjacent terms:

-8/2= -4, 32/-8=-4, -128/32=-4

The ratio of all the adjacent terms is the same and equal to:

r=-4

The first element of the sequence is:

a_1=2

`a_n=a_1\cdot r^(n-1)`

Therefore, the nth term is computed by

r=-4,

`a_n=2(-4)^(n-1)`