Question

What’s is the nth term rule of the
linear sequence below?
-4, -1, 2, 5, 8, . .

Answer 1

`a_(n)` = 3n - 7

Explanation:

the sequence has a common difference between consecutive terms, that is

- 1 - (- 4) = 2 - (- 1) = 5 - 2 = 8 - 5 = 3

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 = 3 , then nth term rule is

`a_(n)` = - 4 + 3(n - 1) = - 4 + 3n - 3 = 3n - 7