13-1

In 13-1 you will be doing sequences. A sequence is a list of numbers. there are two types of sequences: arithmetic and geometric. An arithmetic sequence is a sequence that is generated by adding the same number each time. A geometric sequence is a sequence that is generated by multiplying the same number each time. The formulas for the two sequences are as follows:

geometric sequence

tn= t1 + (n-1)(d)

t1 is the first term. N is the term number. D is the difference, what is being added. Tn is is nth term.

arithmetic sequence

tn= t1 * r^(n-1)

T1 is the first term. R is the term that is being multiplied. N is the term number. Tn is the nth number.

Example 1:

Find a formula for the nth term 3,5,7.

First, you have to figure out if the sequence is arithmetic or geometric. To get from term to term you have to add two, making the sequence arithmetic.

Once you've figured out the type of sequence, you have to use the arithmetic formula to find the nth term.

tn= 3 + (n-1)(2)

tn= 3 + 2n - 2

tn= 2n+1

The formula for the nth term is 2n+1.

Example 2:

Find a formula for the nth term 4,8,16,32

To get from term to term you have to multiply by 2, making it a geometric sequence.

tn= 4 * 2^(n-1)

tn= 4 * 2^n * 2^-1

tn= 4 * 2^n / 2

tn = 2 * 2^n

The formula for the nth term is 2 * 2^n.