Question

Write an explicit formula for an, the nth term of the sequence 6, 14, 22, ....

Answer 1

`a_(n)` = 8n - 2

Explanation:

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

14 - 6 = 22 - 14 = 8

This indicates the sequence is arithmetic with explicit formula

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 6 and d = 8 , then

`a_(n)` = 6 + 8(n - 1) = 6 + 8n - 8 = 8n - 2