Question

Rule for Input/output table Input values: 1, 2, 3, 4, n Output values: -4,-2,0,2

Answer 1

`a_(n)` = 2n - 6

Explanation:

there is a common difference between consecutive terms , that is

- 2 - (- 4) = 0 - (- 2) = 2 - 0 = 2

this indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 4 and d = 2 , then

`a_(n)` = - 4 + 2(n - 1) = - 4 + 2n - 2 = 2n - 6

the rule is then 2n - 6