Graphing+Sequences

**__Graphing Sequences__**
by: Bria and Mr. Rochester

Sequences rely on previous values to derive the next term. Formulas can be generated that will help to find the next term, instead of guessing. Arithmetic sequences involve adding together or subtracting the same number to the previous term in order to get the next term. Geometric sequences are similar to arithmetic sequences with the exception that the operations involved must be multiplication or division. The Recursive formula, helps you find the next term in the sequence, but when you use the Explicit formula, you can use it to find any term in the sequence without depending on the previous term.


 * Example:** //Recursive formula// for a geometric sequence in which the value of the first term is 3.

math A_1=3 math

math A_n=A_{n-1}*3 math

Here we used the formula to find the next three terms of the sequence. We can us the //recursive formula// to find the Explicit formula for this sequence. Using "n", the //explicit// formula for this sequence would be math A_n=3^n math
 * n || An ||
 * 1 || 3 ||
 * 2 || 9 ||
 * 3 || 27 ||
 * 4 || 81 ||
 * n || An ||
 * 1 || 3 ||
 * 2 || 3 x 3= 9 ||
 * 3 || 3 x 3 x 3 = 27 ||
 * 4 || 3 x 3 x 3 x 3 =81 ||

To test our formula, when n= 4, we get math A_4 = 3^4 = 81 math

Our formula works because the fourth term is 81.

We can now graph our formula by graphing the coordinates (1,3) (2,9) (3, 27) (4,81) which we got from our graph.

Graphing our formula connects our points. It also allows us to see that our formula is correct. If our formula was incorrect, then our points would not be on the line.



edited by: Mr. Rochester