Question

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

Answer 1

The number 6 could replace the gap :)

Answer 2

Answer:

Answer is 6

Step-by-step 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