First, find the common difference, or d, for short.
You can find this by subtracting a term from the following one. So for example d = -1 - 4 = -5.
We could have also found d = -6 - (-1) = -5 or d = -11 - (-6) = -5.
Now that we have the common difference, d, we can find a10, a16, ... , or any a(n).
Recognize that we get to a(n) by adding d to a(1) a total of (n-1) times.
For example, to get a(2) we add d to a(1) a total of 2 - 1 = 1 time. To get a(3) we add d 3-1=2 times to a(1).
In general, a(n) = a(1) + (n-1)*d. The last term accomplishes the add d a total of (n-1) times. This even works for a(1), as for us to get a(1) by starting at a(1) we can add d a total of 1 - 1 = 0 times, which makes sense because a(1) = a(1).
So we get a(10) by starting at a(1) and adding d = -5 a total of 9 times.
a(1) = 4, and so
a(10) = 4 - 5*9 = -41, a(16) = 4 - 5*15 = -71, a(20) = 4 - 5*19 = -91, a(25) = 4 - 5*24 = -116, a(29) = 4 - 5*28 = -136.
Hope that helped! Let me know if I can explain this more clearly. Thank you!
