Question

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

an = 13 + (n - 1)(6)

The same sequence has this recursive formula:

an = an - 1 + _____

What number belongs in the blank space in the recursive formula?

Answer 1

The number 6 could replace the gap :)

Answer 2

Answer is 6

Explanation:

Given that there is an arithmetic sequence and has an explicit formula for the nth term as

`a_n =13+(n-1)6\\`

Since n can be any natural number, let us substitute n =1 to find the I term

`a_1 = 13+(1-1)6=13`

Let us find the 2nd term by substituting n=2

`a_2 =13+(2-1)6=19`

Common difference = d=
`a_2-a_1=19-13=6`

Hence from I term a and common difference d, we find the any term can be obtained by adding 6 to the previous term

i.e.
`a_n=a_((n-1) +6)`

6 is the answer