# What is the explicit formula for the sequence? 3, 1, –1, –3, –5, . . .

## -2n+3 n-5 2n-5 -2n+5

Apr 3, 2017

$- 2 n + 5$

#### Explanation:

if by the explicit formula you mean the $n$th term, then it is $- 2 n + 5$.

$3 , 1 , - 1 , - 3 , - 5$ is a linear sequence; the difference between each number is constant.
$1 = 3 = - 2$
$\left(- 1\right) - 1 = - 2$
difference = $- 2$

the difference is the coefficient of $n$, so the $n$th term is $- 2 n +$another number.

$n : 1 , 2 , 3 , 4$
$s : 3 , 1 , - 1 , - 3$

first term:
$n = 1$
$- 2 n = - 2$
$3 - \left(- 2\right) = \left(+\right) 5$

$\therefore n$th term = $- 2 n + 5$