Answer:
4
Step-by-step explanation:
A certain arithmetic sequence has this explicit formula for the nth term:
[tex]a_n = 11 + (n- 1)(4)[/tex]
Substitute n = 1
[tex]a_1 = 11 + (1- 1)(4)[/tex]
[tex]a_1 = 11 [/tex]
Substitute n =2
[tex]a_2 = 11 + (2- 1)(4)[/tex]
[tex]a_2 = 15[/tex]
[tex]d= a_2-a_1=15-11=4[/tex]
So,[tex]a_2=a_1+d=11+4=15[/tex] --1
Substitute n = 3
[tex]a_3 = 11 + (3- 1)(4)[/tex]
[tex]a_3 = 19[/tex]
[tex]a_3=a_2+d=15+4=19[/tex] ---2
So, with 1 and 2
Recursive formula : [tex]a_n=a_{n-1}+d[/tex]
Since d is 4
So, the number belongs in the blank space in the recursive formula is 4.
