Question

Represent the geometric series using the explicit formula. 3, −6, 12, −24, … f(n) = 3 ⋅ (2)(n−1) f(n) = 3 ⋅ (−2)(n−1) f(n) = f(n − 1) ⋅ (2) f(n) = f(n − 1) ⋅ (−2)

Answer 1

Answer:

$f(n)=(-2)(n-1)$

Step-by-step explanation:

Each term of this Geometric Series (3, −6, 12, −24, ...) can also be found through this explicit formula: $f(n)=(-2)(n-1)$ Because the $n^{th}$ term is found by the product of its common ratio "q", times its predecessor n-1. Where n, refers to the order of the term.

So let's test it, suppose we want to find the 4th term. We know the common ratio and the first term. Then we can write f(n) as:

$\\f(n)=3(-2)^{n-1}$

f(4)=f(3)*-2⇒-24=12*-2⇒-24=-24

The explicit formula is ok.