Mathematics: If tn = 4n+1, find t1, t2, t3, and tn+1. express tn+1−tn in its simplest form. [arithmetic sequences]

I believe it would be $3Step-by-step explanation:...

If tn = 4n+1, find t1, t2, t3, and tn+1. express tn+1−tn

whityelaine7997

11.01.2022

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:

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

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

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