Question

explicit rule for -8, -2, 4, 10, 16

Answer 1

add 6

Answer 2

Differences:
6, 6, 6, 6 -> Linear

y = mx + b

Need m, b

-8 = m(1)+b
2 = m(2)+b

-8 = m + b
2 = 2m + b

Now, solve for m and b.

m = -8 - b

2 = 2(-8-b)+b
2 = -16 - 2b + b = -16 - b

2 = -16 - b
14 = -b

b = -14

m = -8 - b -> m = -8 + 14 = 6

y = 6x - 14

CHECK

-8 = 6 - 14... YES

Answer 3

\(a_{n+1} = a_n + 6\)