Question

Determine the explicit equation for the arithmetic sequence given below.-3,-7,-11,-15,-19

Answer 1

-3 + (n-1)(-4)

Explanation:

We follow the formula.

a1 + (n-1)d

d is the common difference.

Answer 2

-4n + 1

Explanation:

-3, - 7, -11 , -15 ,-19 ,.........

`a_(1) = -3\\\\`

Common difference (d) = 2nd term - first term

d = -7 -(-3)

= -7 + 3

d = -4

`a_(n) =a + (n-1)d\\\\a_(n) = -3 + (n - 1)(-4)`

= -3 + n *(-4) - 1*(-4)

= -3 - 4n + 4

= -4n + 1