The closed form of the sequence [0,0,0,1,2,4,8,16,.....] is [tex]a_n = 2^{n-1}[/tex]
How to determine the closed form?
The sequence is given as:
[0,0,0,1,2,4,8,16,.....]
Remove the leading zeros
[1,2,4,8,16,.....]
The above sequence is a geometric sequence, with the following parameters:
- First term, a₁ = 1
- Common ratio, r = 2
The closed form is calculated using:
[tex]a_n = a_1 * r^{n-1}[/tex]
Substitute the known values
[tex]a_n = 1 * 2^{n-1}[/tex]
Evaluate the product
[tex]a_n = 2^{n-1}[/tex]
Hence, the closed form of the sequence [0,0,0,1,2,4,8,16,.....] is [tex]a_n = 2^{n-1}[/tex]
Read more about sequence at:
https://brainly.com/question/6561461
#SPJ1
