EXPLANATION
Given the sequence t_n = 3.5n + 4.5
In order to know if 85 is a term of this relationship we must apply the following relationship:
85 = 3.5*n + 4.5
Subtracting -4.5 to both sides:
85 - 4.5 = 3.5n +4.5 -4.5
Simplifying:
80.5 = 3.5 n
Dividing both sides by 3.5:
80.5 / 3.5 = 3.5/3.5 n
Simplifying:
23 = n
So, when n=23, then t_n = 85
So, 85 is a term of this sequence.
t_n = 3.5n + 4.5
t_n+1 = 3.5(n+1) + 4.5
t_n+1 - t_n = 3.5(n+1) + 4.5 - 3.5n - 4.5
Simplifying:
t_n+1 - t_n = 3.5(n+1) - 3.5n
Factor out 3.5 as common factor:
t_n+1 - t_n = 3.5 [n+1 - n]
Simplifying:
t_n+1 - t_n = 3.5 (1) = 3.5
So, t_n+1 - t_n = 3.5