Question

PLEASE HELP ASAP! ! ! ! ! ! !

What is the explicit rule for this geometric sequence? 2/9,2/3,2,6.....

an = 2/9 × 3^n-1

an = 3 (2/9)^n-1

an = 2/9 × 3^n

an = 3 (2/9)^n

Answer 1

Answer:

1. $a_n=(\frac{2}{9})\times 3^{(n-1)}$

Step-by-step explanation:  

Since we know that an explicit formula for geometric sequence is in form $a_n=(a_1)\cdot r^{n-1}$, where,

$a_n$= nth term of geometric sequence.

$a_1$= 1st term of the geometric sequence.

$r$= Common ratio of the sequence.

We can see that 1st term of our geometric sequence is $\frac{2}{9}$. Let us find common ratio of our given sequence by dividing any number by its preceding number in the sequence.

Let us divide 6 by 2 as 2 is preceding number of 6 in our given geometric sequence.

$r=\frac{6}{2}$

$r=3$

We can see that common ratio is 3.

Upon substituting our values in explicit formula of geometric sequence we will get,

$a_n=(\frac{2}{9})\times 3^{(n-1)}$  

Therefore, the explicit formula for our given geometric sequence will be $a_n=(\frac{2}{9})\times 3^{(n-1)}$ and 1st option is the correct choice.

Answer 2

Answer:

an = 2/9 × 3^n-1