Question

What is the rule for the following geometric sequence? 64,128,256,512...

a) a_(n) = 64(-2)^n-1
b) a_(n) = 64(2)^n-1
c) a_(n) = 64(1/2)^n-1
d) a_(n) = 64(-1/2)^n-1

Answer 1

B

Explanation:

The explicit rule for 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 =
`(a_(2) )/(a_(1) )` =
`(128)/(64)` = 2 , then

`a_(n)` = 64
`(2)^(n-1)` → B

Answer 2

b).

`{ \tt{a _(n) = a( {r}^(n - 1) )}} \\ { \tt{a _(n) = 64( {2}^(n - 1)) }}`