Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Enter the explicit rule for the geometric sequence.

9, 6, 4, 8/3,…

Answer 1

9 (2/3) ^n-1

Explanation:

i took the test

Answer 2

Answer:
`\bold{a_n=(2^(n-1))/(3^(n+1))}`

Explanation:

The explicit rule for a geometric sequence is:
`a_n=a_1(r)^(n-1)\quad \text{where}\ a_1\ \text{is the first term and r is the common ratio}`

Given the sequence {9, 6, 4,
`(8)/(3)`, ... } we know

• the first term (a₁) is 9
• the common ratio (r) is
  `(6)/(9)=(2)/(3)\ \text{when simplified}`

So, the explicit rule for the given sequence is:

`a_n=9\bigg((2)/(3)\bigg)^(n-1)\\\\\\.\quad =3\cdot3((2)^(n-1))/((3)^(n-1))\\\\\\.\quad =3((2)^(n-1))/((3)^(n))\\\\\\.\quad =((2)^(n-1))/((3)^(n+1))`