# How do you write the expression for the nth term of the sequence given 2, -4, 6, -8, 10,...?

May 4, 2017

detail in explanation

#### Explanation:

case 1 you know how much is n
1.n is odd number then

$A n = 2 + \left(n - 1\right) \cdot 2$

2.n is even number then

$A n = - 4 + \left(n - 2\right) \cdot \left(- 2\right)$

case 2. n is unknown

$A n = \left(2 + 2 \cdot \left(n - 1\right)\right) \cdot {\left(- 1\right)}^{n - 1}$