Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.){1/2,1/4,1/6,1/8,1/10,...}a_n = ?
Accepted Solution
A:
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......