Question

What is the recursive formula when given the explicit formula for the following geometric sequence?

Answer 1

Answer:

C

Step-by-step explanation:

Take a careful look at a(n) =  6(-8)^(n-1).

The first term is 6.  This is the result if we let n = 1; 6(-8)^0 = 6(1) = 6.  Thus, we can immediately eliminate possible answer choices A and D.

What's the next term?  Knowing that the first term, a(1), is 6, the next term is found by multiplying this 6 by (-8)^1, obtaining -48.

The next (third) term is found by multiplying this -48 by (-8)^2, obtaining -48*(+64), or - 3072.

Note that the sign of (-8)^(n-1) alternates, being odd when n-1 is odd and even when n-1 is even.

Answer C is the correct one.