Question

1, ½, 0, ...; 16th term

Answer 1

a₁₆ = -
`(13)/(2)`

Explanation:

there is a common difference between consecutive terms in the sequence, that is

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

0 -
`(1)/(2)` = -
`(1)/(2)`

this indicates the sequence is arithmetic with nth term formula

`a_(n)` = a₁ + d(n - 1)

where a₁ is the first term , d the common difference , n the term number

here a₁ = 1 , d = -
`(1)/(2)` , n = 16 , then

a₁₆ = 1 + (-
`(1)/(2)` × 15 ) = 1 + (-
`(15)/(2)` ) =
`(2)/(2)` -
`(15)/(2)` = -
`(13)/(2)`