Question

What is the recursive formula for this geometric sequence? –4, –24, –144, –864, ...

Answer 1

the question does not present the options, but this does not interfere with the resolution

Let

a1=-4

a2=-24

a3=-144

a4=-864

a5=?

we know that

a2/a1=-24/-4----> 6-------> a2=6*a1

a3/a2=-144/-24---> 6-----> a3=6*a2

a4/a3=-864/-144---> 6----> a4=6*a3

therefore

a5=6*a4-----> a5=6*(-864)------> a5=-5184

hence 

the formula is

an=6*a(n-1)

n and (n-1) are subscripts