Question

What is the recursive formula for this geometric sequence -2, -16, ...

Answer 1

`\displaystylea_1=-2\\r=8\\a_n=8a_(n-1)\\\\\left \{ {{a_1=-2} \atop {a_n=8a_(n-1)}} \right.`

Answer 2

Answer: The sequence is: An = -2*8^(n-1)

Explanation:

 geometric sequence is of the form:

An = a*r^(n-1)

where can be any positive integer number.

here the first two numbers are -2 and -16, so we have that:

A1 = a*r^(0) = a = -2

now, we know that our sequence is of the form:

An = -2*r^(n-1)

now, for n= 2 we have that:

A2 = -2*r^(1) = -2*r = -16

r = -16/-2 = 8

now we have determinated our sequence:

An = -2*8^(n-1)