Question

F(1)=192
192,48,12,3

The sequence shown is

Answer 1

Geometric

an=an-1₋(.25);a₁=192

an=192(.25)^n-1

7.32421875*10^−4

Explanation:

Answer 2

The sequence shown is geometric

Recursive function:

`a_(n) = a_(n-1)* r`

with
`a_1 = 192`

Explicit function:
`a_n = 192 * 0.25^(n-1)`

10th term: 0.000732421876

Explanation:

In a geometric sequence the n+1 term divide by the n term is constant

48/192 = 0.25

12/48 = 0.25

3/12 = 0.25

From this result we can deduce the recursive function:

`a_(n) = a_(n-1)* r`

with
`a_1 = 192`

Explicit function:

`a_n = a * r^(n-1)`

where a is the first term in the sequence (= 192) and r is the common ratio (= 0.25). Replacing:

`a_n = 192 * 0.25^(n-1)`

The 10th term is:

`a_(10) = 192 * 0.25^9 = 0.000732421876`