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

[arithmetic sequences]

Step-by-step explanation:

We have that:

When we substitute n=1, we get:

When we substitute n=2 we get:

When we substitute n=3, we get:

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

Now

We expand and simplify to obtain:

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.