Question

Enter the explicit rule for the geometric sequence.

120, 40, 40/3, 40/9, 40/27, ...

I know the first part would be but i dont know what would be put in the middle of the parenthesis so if anyone could please help that would be awesome ty!

an= 120( )^n-1

Answer 1

an = 120(1/3)^(n-1)

because it divides by 3 to get the next number

Answer 2

`a_(n)=120((1)/(3))^(n-1)`

Explanation:

The given geometric sequence is 120, 40, 40/3, 40/9.........n terms.

As we know nth term of a geometric sequence is represented as

`a_(n)=a(r)^(n-1)`

Here a(n) = nth term

a = first term

r = common ratio

n = number of terms

In this sequence a = 120

r = second term/first term = 40/120 = 1/3

Therefore the sequence can be represented as

`a_(n)=120((1)/(3))^(n-1)`

Explicit rule of the geometric sequence is

`a_(n)=120((1)/(3))^(n-1)`