Question

The first two terms of a geometric sequence are a1 = 1/3 and a2 = 1/6. What is a8, the eighth term?

A. 1/256
B. 1/384
C. 1/768
D. 1/128 10 points

Answer 1

B. 1/384

Explanation:

a1=1/3

a2 = 1/6

The constant factor is 1/2

a1=2/3*1/2

a2=2/3*1/2^2

a8=2/3*(1/2)^8

2/3*1/256

Answer 2

B

Explanation:

Given the sequence is geometric then the common ratio r is

r =
`(a_(2) )/(a_(1) )` =
`((1)/(6) )/((1)/(3) )` =
`(1)/(2)`

The n th term of a geometric sequence is

`a_(n)` =
`a_(1)`
`(r)^(n-1)`

=
`(1)/(3)` ×
`((1)/(2)) ^(7)`

=
`(1)/(3)` ×
`(1)/(128)` =
`(1)/(384)`