What is the nth term rule of the linear sequence below?
−5,−2,1,4,7,...

= 3n - 8

Step-by-step explanation:

Note the common difference d between consecutive terms, that is

d = - 2 - (- 5) = 1 - (- 2) = 4 - 1 = 7 - 4 = 3

This indicates the sequence is arithmetic with n th term

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 5 and d = 3, thus

= - 5 + 3(n - 1) = - 5 + 3n - 3 = 3n - 8

n

step-by-step explanation: