Question

A certain arithmetic sequence has this explicit formula for the nth term:

an = 11 + (n - 1)(4)
The same sequence has this recursive formula:
an = an-1 +__
What number belongs in the blank space in the recursive formula?

Answer 1

The answer is 4

Explanation:

Answer 2

4

Explanation:

The n th term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given

`a_(n)` = 11 +(n - 1)4 , then

d = 4

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

`a_(n)` =
`a_(n-1)` + 4