Question

Write an explicit formula for an the nth term of the sequence 40, 33, 26

Answer 1

`a_(n)` = - 7n + 47

Explanation:

there is a common difference between consecutive terms , that is

33 - 40 = 26 - 33 = - 7

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 = 40 and d = - 7 , then

`a_(n)` = 40 - 7(n - 1) = 40 - 7n + 7 = - 7n + 47