Question

Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1? 3, –6, 12, –24, 48

Answer 1

Answer:

Step-by-step explanation:

f(1)=a=3

first term,a=3

common ratio,r=-6/3

r=-2

general term of an gp=a(r)^n-1

formula=3×(-2)^n-1

Answer 2

The recursive formula can be used to generate the given sequence:

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

Explanation:

The given sequence : 3, –6, 12, –24, 48

First term : f(1)= 3

Since , the sequence is increasing exponentially with the common ratio between the terms= $r=\dfrac{-6}{3}=-2$

Recursive formula for geometric sequence :

$f(n+1)=rf(n)$

Therefore , the recursive formula can be used to generate the given sequence:

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

# Learn more :

Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1?

6, 1, –4, –9, –14, …

f (n + 1) = f(n) + 5

f (n + 1) = f(n) – 5

f (n) = f(n + 1 ) – 5

f (n + 1) = –5f(n)