Question

An arithmetic sequence has this explicit formula: an = 14 + (n - 1)3. What is the recursive formula?​

Answer 1

`a_(n)` =
`a_(n-1)` + 3 with a₁ = 14

Explanation:

The explicit formula for an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference, then

`a_(n)` = 14 + (n - 1)3

has a₁ = 14 and d = 3

A recursive formula allows a term in the sequence to be found by adding d to the previous term, thus recursive formula is

`a_(n)` =
`a_(n-1)` + 3 , with a₁ = 14