Question

Which equation represents the nth term of the sequence {2, -1, -4, -7,...}?

Answer 1

`a_(n)` = 5 - 3n

Explanation:

There is a common difference between consecutive terms, that is

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

This indicates the sequence is arithmetic with n th term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = - 3 , thus

`a_(n)` = 2 - 3(n - 1) = 2 - 3n + 3 = 5 - 3n