Question

HELP!Please solve! this!!

Answer 1

Answer:

Recursive formula for geometric sequence

$a_{n}=a_{n-1}\times r$

is $a_{n}=a_{n-1}\times 6$

and explicit formula for geometric sequence $a_{n}=a_{1}^{r-1}$ is

$a_{n}=(\frac{1}{2})^{6-1}$

Step-by-step explanation:

Given sequence is $\frac{1}{2},3,18,108,648,...$

To find the recursive and explicit formula for this sequence:

Let $a_{1}=\frac{1}{2},a_{2}=3,a_{3}=18,a_{4}=108,a_{5}=648,...$

To find the common ratio r:

$r=\frac{a_{2}}{a_{1}}$

$=\frac{3}{\frac{1}{2}}$

$=3\times 2$

$=6$

Therefore r=6

$r=\frac{a_{3}}{a_{2}}$

$=\frac{18}{3}$

$=6$

Therefore r=6

Therefore the common ration r=6

Therefore the given sequence is geometric sequence

Recursive formula for geometric sequence is $a_{n}=a_{n-1}\times r$

$a_{n}=a_{n-1}\times 6$

and explicit formula is $a_{n}=a_{1}^{r-1}$

$a_{n}=(\frac{1}{2})^{6-1}$

$=(\frac{1}{2})^{5}$

$=\frac{1}{32}$

Therefore $a_{n}=\frac{1}{32}$

Answer 2

Answer:

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

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

Step-by-step explanation:

3 = 6 × ½

18 = 6 × 3

.

.

.

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