Arithmetic,Geometric

Question

Given the geometric sequence 

Which of the following formulas represents the explicit formula for this sequence?

A an=2⋅(3)(n−1)

B an=3⋅(2)n−1

C an=2⋅(3)n−1

D an=3⋅(2)(n−1)

Answer 1

D) is a geometric sequence with a1 = 3, r=2=common ratio

its terms are:

a1=3

a2=6

a3=12

a4=24

a5=48

...

an=3(2)^(n-1)

A) is a geometric sequence with a1 = 2, r=3=common ratio

its terms are

a1 =2

a2=6

a3=18

a4=54

a5=112

...

an=2(3)^(n-1)

B) and C) are not geometric or arithmetic sequences

B) is 3(2)^n -1

a1 = 5

a2 = 11

a3 = 23

a4 = 47

a5 = 95

...

C) is 2(3)^n -1

a1 = 5

a2 = 17

a3 = 53

a4 = 161

a5 = 1457

...