Answer:
[tex]a_{n}=\frac{1}{2n}[/tex] [Where a ≥ 1 ]
Step-by-step explanation:
The pattern of the given sequence is {[tex]\frac{1}{2},\frac{1}{4},\frac{1}{6},\frac{1}{8},\frac{1}{10},......[/tex]
We have to find a formula for the general term [tex]a_{n}[/tex] of the given sequence.
We can rewrite the terms of the sequence as
[tex]\frac{1}{2}=\frac{1}{(2)(1)}[/tex]
[tex]\frac{1}{4}=\frac{1}{(2)(2)}[/tex]
[tex]\frac{1}{6}=\frac{1}{(2)(3)}[/tex]
[tex]\frac{1}{8}=\frac{1}{(2)(4)}[/tex]
[tex]\frac{1}{10}=\frac{1}{(2)(5)}[/tex]
Now we can write the term [tex]a_{n}[/tex] as
[tex]a_{n}=\frac{1}{2n}[/tex]
Where n = 1, 2, 3, 4, 5......
