Question

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

Answer 1

Answer:

common ration = 1/4

12th term = 1/65536

Step-by-step 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

Answer 2

Answer:

see explanation

Step-by-step explanation:

The common ratio r is calculated as

$\frac{a_{2} }{a_{1} }$ = $\frac{16}{64}$ = $\frac{1}{4}$

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 = $\frac{1}{4}$ , thus

$a_{12}$ = 64 × $(\frac{1}{4}) ^{11}$ = 64 × $\frac{1}{4194304}$ = $\frac{64}{4194304}$ = $\frac{1}{65536}$