148k views
0 votes
What is the recursive rule for this geometric sequence?

3, 3/2, 3/4, 3,8,...

choices -
a1= 1/2;an = 3/2 x an - 1
a1= 3/2;an = 1/2 x an -1
a1= 3; an = 1/2 x an -1
a1= 1/2;an = 3x an -1

please explain your answer, if you can

User Rohaq
by
8.4k points

2 Answers

5 votes
The objective here is to find
r (so called common ratio):

r=a_(n)/a_(n-1)=a_(2)/a_(1)= (3)/(2) : 3 = (3)/(2) * (1)/(3) = (1)/(2)
So assuming the first element of sequence is 3 (as you mentioned) we now can define the recursive rule for this geometric sequence:

a_(1)=3; a_(n)=(1)/(2)a_(n-1)
User AkshayJ
by
8.2k points
1 vote

Answer:

C.
a_1=3,a_n=(1)/(2)a_(n-1),n\geq 2

Explanation:

We are given that


3,(3)/(2),(3)/(4),(3)/(8),..

We have to find the recursive formula rule for this geometric sequence.


a_1=3


a_2=(3)/(2)


a_2=3* (1)/(2)=(1)/(2)* a_1


a_3=(3)/(4)


a_3=(1)/(2)* (3)/(2)


a_3=(1)/(2)* a_2


a_4=(3)/(8)


a_4=(1)/(2)* (3)/(4)


a_4=(1)/(2)* a_3

Therefore, the recursive rule


a_1=3,a_n=(1)/(2)a_(n-1),n\geq 2

Option C is true

User Alberto Moro
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories