Question

Write an explicit formula for the sequence... then find a17

Answer 1

Answer: The correct one is an=5/2n-11/2,37 so A :)

Answer 2

The correct answer option is:
`a_n=(5)/(2) n-(11)/(2), 37`.

Explanation:

We are given the following arithmetic sequence and we are to write an explicit formula for it and the find the 17th term of the sequence:

{
`a_n`}={
`-3, -(1)/(2) ,2,(9)/(2) ,7`}

From the given options, we can put in the values of n and check if it proves to be true.

For
`a_n=(5)/(2) n-(11)/(2)`, put values of
`n` from 1 to 5 which the number of the term.

`a_1=(5)/(2) (1)-(11)/(2)\\\\a_1=-3`

`a_2=(5)/(2) (2)-(11)/(2)\\\\a_2=-(1)/(2)`

`a_3=(5)/(2) (3)-(11)/(2)\\\\a_3=2`

`a_4=(5)/(2) (4)-(11)/(2)\\\\a_4=(9)/(2)`

`a_5=(5)/(2) (5)-(11)/(2)\\\\a_5=7`

Therefore, the formula for the given sequence is
`a_n=(5)/(2) n-(11)/(2)`.

Also,
`a_(17)=(5)/(2) (17)-(11)/(2)=37`