13 - 1

This past week we started chapter thirteen. It is about sequences. You have to determine whether or not it is geometric, or arithmetic. There are formulas that you use to determine this. They are:

Arithmetic – tn = t1 + (n – 1)d
Geometric – tn = t1 x r^n-1

Example 1:
Determine whether the sequence is geometric, arithmetic, or neither and find a formula.
17, 21, 25, 30. . .
It is neither because you do not subtract or add the same number every time. You cannot find a formula, because it is neither geometric or arithmetic.

Example 2:
Determine whether the sequence is geometric, arithmetic, or neither and find a formula.
4, 6, 8, 10, 12. . .

This sequence is arithmetic because you add 2 every time. To find the formula, you plug into the arithmetic formula. d = 2, because that is the number you add everytime.

Tn = 4 + (n- 1)2
Tn= 4 + 2n -2
Tn =2 + 2n <--the formula you find.

Example 3:
Determine whether the sequence is geometric, arithmetic, or neither and find a formula.
16, 8, 4, 2. . .

This sequence is geometric because if you put 2 over 4, 4 over 8, and 8 over 16, you get ½. r = ½, because that is the number you multiply by to get the sequence.
Tn = 16 x (1/2) ^n-1 <--the formula you find.