Question

Trying to figure out if the sequence is arithmetic or not.

Answer 1

In order to find if the sequence

`a_n=(1)/(3+8n)`

let's calculate some terms of the sequence given using the formula above

`a_1=(1)/(3+8(1))=(1)/(3+8)=(1)/(11)`
`a_2=(1)/(3+8(2))=(1)/(3+16)=(1)/(19)`
`a_3=(1)/(3+8(3))=(1)/(3+24)=(1)/(27)`

The using the terms we found

If the difference between 1/19-1/11 is equal to 1/27-1/19 is equal therefore we have an arithmetic sequence

`a_2-a_1=(1)/(19)-(1)/(11)=-(8)/(209)`
`a_3-a_2=(1)/(27)-(1)/(19)=-(8)/(513)`

As we can see they are different therefore the sequence is not arithmetic