Question

Find the common ratio and the 12th term of the geometric sequence 64, 16, 4, ...​

Answer 1

see explanation

Explanation:

The common ratio r is calculated as

`(a_(2) )/(a_(1) )` =
`(16)/(64)` =
`(1)/(4)`

The n th term of a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = 64 and r =
`(1)/(4)` , thus

`a_(12)` = 64 ×
`((1)/(4)) ^(11)` = 64 ×
`(1)/(4194304)` =
`(64)/(4194304)` =
`(1)/(65536)`

Answer 2

common ration = 1/4

12th term = 1/65536

Explanation:

64

64*1/4 = 16

16 * 1/4 = 4

4* 1/4 = 1

1 * 1/4 = 1/4

1/4*1/4 = 1/16

1/16*1/4 = 1/64

etc

1/256

1/1024

1/4096

1/16384

12th term = 1/65536