Question

Write an explicit formula for an, the nth term of the sequence 11,2,-7

Answer 1

`a_(n)` = 20 - 9n

Explanation:

There is a common difference d between consecutive terms, that is

d = 2 - 11 = - 7 - 2 = - 9

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 = 11 and d = - 9 , then

`a_(n)` = 11 - 9(n - 1) = 11 - 9n + 9 = 20 - 9n