Question

Write an explicit formula for an, the nth term of the sequence 35, 38, 41, ...

Answer 1

`a_(n)` = 3n + 32

Explanation:

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

d = 38 - 35 = 41 - 38 = 3

This indicates the sequence is arithmetic with n th term ( explicit formula )

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 35 and d = 3 , then

`a_(n)` = 35 + 3(n - 1) = 35 + 3n - 3 = 3n + 32