Question

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

Answer 1

Answer:   $\bold{a_n=\dfrac{2^{n-1}}{3^{n+1}}}$

Step-by-step 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, $\dfrac{8}{3}$, ... } we know

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

So, the explicit rule for the given sequence is:

$a_n=9\bigg(\dfrac{2}{3}\bigg)^{n-1}\\\\\\.\quad =3\cdot3\dfrac{(2)^{n-1}}{(3)^{n-1}}\\\\\\.\quad =3\dfrac{(2)^{n-1}}{(3)^{n}}\\\\\\.\quad =\dfrac{(2)^{n-1}}{(3)^{n+1}}$