Question

Find the Nth Term: 2, -6, -14, -22.
Thanks.

Answer 1

`a_(n)` = - 8n + 10

Explanation:

there is a common difference between consecutive terms , that is

- 6 - 2 = - 14 - (- 6) = - 22 - (- 14) = - 8

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 = 2 and d = - 8 , then

`a_(n)` = 2 - 8(n - 1) = 2 - 8n + 8 = - 8n + 10