Answer:
[tex]T_n = \frac{1}{4^{n-1}}[/tex]
Step-by-step explanation:
Given
[tex]({)1, 1/4, 1/16, 1/64, 1/256, ... (})[/tex]
Required
The general term
The given sequence is geometric.
So first, we calculate the common ratio (r)
[tex]r = T_2/T_1[/tex]
So, we have:
[tex]r = 1/4 \div 1[/tex]
[tex]r = 1/4[/tex]
The function is then calculated using:
[tex]T_n =T_1 * r^{n-1}[/tex]
This gives
[tex]T_n =1 * 1/4^{n-1}[/tex]
[tex]T_n = \frac{1}{4^{n-1}}[/tex]
