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

Question

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

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Answer 1 · 2017-04-03T20:45:39

$-2n+5$

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

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

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

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

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

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