Question

If tn = 4n+1, find t1, t2, t3, and tn+1. Express tn+1−tn in its simplest form.

Answer 1

Answer:

$t_1=5$

$t_2=9$

$t_3=13$

$t_{n+1}-t_n=4$

Step-by-step explanation:

We have that:

$t_n=4n+1$

When we substitute n=1, we get:

$t_1=4*1+1=5$

When we substitute n=2 we get:

$t_2=4*2+1=9$

When we substitute n=3, we get:

$t_3=4*3+1=13$

When we substitute n=n+1, we get:

$t_{n+1}=4*(n+1)+1=4n+5$

Now

$t_{n+1}-t_n=4n+5-(4n+1)$

We expand and simplify to obtain:

$t_{n+1}-t_n=4n+5-4n-1$

$t_{n+1}-t_n=4$