If tn=3n+4, find t1, t2, t3, and tn+1. Express tn+1−tn in its simplest form.
just plug in n=1,2,3
t1 = 3*1+4 = 7
and so on
t_n+1 = 3(n+1)+4
t_n = 3n+4
subtract and you get 3
To find the values of t1, t2, t3, and tn+1 using the given formula tn = 3n + 4, we substitute the values of n into the formula.
t1 = 3(1) + 4 = 3 + 4 = 7
t2 = 3(2) + 4 = 6 + 4 = 10
t3 = 3(3) + 4 = 9 + 4 = 13
Now, let's find tn+1. Given that tn = 3n + 4, we substitute n+1 for n to find tn+1.
tn+1 = 3(n + 1) + 4
= 3n + 3 + 4
= 3n + 7
Therefore, tn+1 = 3n + 7.
To find tn+1 − tn, we substitute the values of tn and tn+1 into the expression.
tn+1 − tn = (3n + 7) − (3n + 4)
= 3n + 7 − 3n - 4
= (3n - 3n) + (7 - 4)
= 0 + 3
= 3
Therefore, tn+1 − tn = 3.