Question

HELP!Please solve! this!!

Answer 1

Recursive: a(n) = 6a(n-1)

Explicit: a(n) = (6^n)/12

Explanation:

3 = 6 × ½

18 = 6 × 3

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Recursive formula:

a(n) = 6a(n-1)

Explicit:

a(n) = a × r^(n-1)

a(n) = ½ × 6^(n-1)

a(n) = (6^n)/12

Answer 2

Recursive formula for geometric sequence

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

is
`a_(n)=a_(n-1)* 6`

and explicit formula for geometric sequence
`a_(n)=a_(1)^(r-1)` is

`a_(n)=((1)/(2))^(6-1)`

Explanation:

Given sequence is
`(1)/(2),3,18,108,648,...`

To find the recursive and explicit formula for this sequence:

Let
`a_(1)=(1)/(2),a_(2)=3,a_(3)=18,a_(4)=108,a_(5)=648,...`

To find the common ratio r:

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

`=(3)/((1)/(2))`

`=3* 2`

`=6`

Therefore r=6

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

`=(18)/(3)`

`=6`

Therefore r=6

Therefore the common ration r=6

Therefore the given sequence is geometric sequence

Recursive formula for geometric sequence is
`a_(n)=a_(n-1)* r`

`a_(n)=a_(n-1)* 6`

and explicit formula is
`a_(n)=a_(1)^(r-1)`

`a_(n)=((1)/(2))^(6-1)`

`=((1)/(2))^(5)`

`=(1)/(32)`

Therefore
`a_(n)=(1)/(32)`