Answer:
Geometric
an=an-1₋(.25);a₁=192
an=192(.25)^n-1
7.32421875*10^−4
Step-by-step explanation:
Answer:
The sequence shown is geometric
Recursive function:
[tex]a_{n} = a_{n-1}\times r[/tex]
with [tex]a_1 = 192[/tex]
Explicit function: [tex]a_n = 192 \times 0.25^{n-1} [/tex]
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:
[tex]a_{n} = a_{n-1}\times r[/tex]
with [tex]a_1 = 192[/tex]
Explicit function:
[tex]a_n = a \times r^{n-1} [/tex]
where a is the first term in the sequence (= 192) and r is the common ratio (= 0.25). Replacing:
[tex]a_n = 192 \times 0.25^{n-1} [/tex]
The 10th term is:
[tex]a_{10} = 192 \times 0.25^9 = 0.000732421876 [/tex]
