Question

F(1)=192 192,48,12,3 The sequence shown is

Answer 1

Answer:

Geometric

an=an-1₋(.25);a₁=192

an=192(.25)^n-1

7.32421875*10^−4

Step-by-step explanation:

Answer 2

Answer:

The sequence shown is geometric

Recursive function:

$a_{n} = a_{n-1}\times r$

with $a_1 = 192$          

Explicit function: $a_n = 192 \times 0.25^{n-1}$

10th term: 0.000732421876

Step-by-step 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:

$a_{n} = a_{n-1}\times r$

with $a_1 = 192$          

Explicit function:

$a_n = a \times r^{n-1}$

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

$a_n = 192 \times 0.25^{n-1}$

The 10th term is:

$a_{10} = 192 \times 0.25^9 = 0.000732421876$