Explicit Pattern Rule for Math

When the question asks for a really high term, for example the 20th term, we are faced with 2 choices.

Choice # 1 is to continue the pattern until you get to the 20th term.  Now that is time consuming and full of places where you can lose track.  I suggest choice #2, the explicit pattern rule!

Choice #2  The explicit pattern rule

To find the 20th term = 1st number in pattern + [(term number minus 1) x difference]

Let's see an example.

1, 4, 7, 10, 13,

Find the 20th term!!!!!

First thing is to find the difference (This is the magical word).

The difference between the terms is 3.

Now we use the explicit pattern rule to find the 20th term.  (They are asking what the 20th number in the pattern might actually be)

20th = 1 + [(20-1) x 3]

       = 1 + (19 x 3)

       = 1 + 57

       = 58

New pattern

2, 7, 12, 17

What is the 40th term!!!!  Ahhhhhhhh!!!!

First thing is to find the difference.  The difference is 5.

Now we use the explicit pattern rule to find the 40th term.

40th = 2 + (39 x 5)

       = 2 + 195

       = 197

The key is to do the multiplying first because of order of operations. 

Simple.