Question

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 = ?

Answer 1

`a_(n)=(1)/(2n)` [Where a ≥ 1 ]

Explanation:

The pattern of the given sequence is {
`(1)/(2),(1)/(4),(1)/(6),(1)/(8),(1)/(10),......`

We have to find a formula for the general term
`a_(n)` of the given sequence.

We can rewrite the terms of the sequence as

`(1)/(2)=(1)/((2)(1))`

`(1)/(4)=(1)/((2)(2))`

`(1)/(6)=(1)/((2)(3))`

`(1)/(8)=(1)/((2)(4))`

`(1)/(10)=(1)/((2)(5))`

Now we can write the term
`a_(n)` as

`a_(n)=(1)/(2n)`

Where n = 1, 2, 3, 4, 5......