Answer:
[tex]t_1=5[/tex]
[tex]t_2=9[/tex]
[tex]t_3=13[/tex]
[tex]t_{n+1}-t_n=4[/tex]
Step-by-step explanation:
We have that:
[tex]t_n=4n+1[/tex]
When we substitute n=1, we get:
[tex]t_1=4*1+1=5[/tex]
When we substitute n=2 we get:
[tex]t_2=4*2+1=9[/tex]
When we substitute n=3, we get:
[tex]t_3=4*3+1=13[/tex]
When we substitute n=n+1, we get:
[tex]t_{n+1}=4*(n+1)+1=4n+5[/tex]
Now
[tex]t_{n+1}-t_n=4n+5-(4n+1)[/tex]
We expand and simplify to obtain:
[tex]t_{n+1}-t_n=4n+5-4n-1[/tex]
[tex]t_{n+1}-t_n=4[/tex]
