Question

Write an explicit formula for an the nth term of the sequence 6, 12, 18

Answer 1

`a_(n)` = 6n

Explanation:

there is a common difference between consecutive terms, that is

12 - 6 = 18 - 12 = 6

this indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 6 and d = 6 , then

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