Question

Write an explicit formula for an, the nth term of the sequence 23, 19, 15, ....

Answer 1

`a_(n)` = - 4n + 27

Explanation:

there is a common difference between consecutive terms, that is

19 - 23 = 15 - 19 = - 4

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 = 23 and d = - 4 , then

`a_(n)` = 23 - 4(n - 1) = 23 - 4n + 4 = - 4n + 27 or 27 - 4n