Question

A certain arithmetic sequence has the following explicit formula for the nth term: an = 4 + (n - 1)(7) The same sequence has the following recursive formula: an = an-1 + _____ What number belongs in the blank space in the recursive formula?

Answer 1

an = 4 + (n - 1)(7)

a1 = 4 + (1-1)*7 = 4
a2 = 4 + (2-1)*7 = 4 + 7


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

7 is common difference of arithmetic sequence.

Answer 2

Answer:
`a_n=a_(n-1)+7`

Explanation:

We know that the nth term in Arithmetic sequence is given by :-

`a_n=a+(n-1)d`..................(1)

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

`a_n=4+(n-1)(7)`.............................(2)

When we compare (1) and (2), we get

`d=7`

Also, the recursive formula in A.P. can be written as

`a_n=a_(n-1)+d`

Therefore, The same sequence has the following recursive formula:

`a_n=a_(n-1)+7`