Sequences

A sequence is a list of numbers. (2,4,6,8...)

Now that we have that established,

There are two types of Sequences: Arithmetic and Geometric.

An Arithmetic sequence made by adding the same positive or negative integer each time to the previous term to generate a list.

The formula is:

tn=t1+(n-1)d

Where:

t1=first term

n=term #

d=difference

tn=the nth term

A Geometric sequence is made by mulitiplying by the same whole number or fraction to the previous term.

Fromula:

tn=t1 * r ^(n-1)

Where:

r=ratio the number that is mulitiplied to the terms

t1=first term

n=the term number

EX1

Find the first 4 terms of the sequence tn=4n+3 and state whether it is geometric or arithmetic.

t1 = 4(1)+3=7

t2 = 4(2)+3=11

t3 = 4(3)+3=15

t4 = 4(4)+3=19

7, 11, 15, 19... We can see that you are adding 4 to each term, so it is arithmetic.

EX2 Find the formula for 3, 6, 12, 24...

You multiply by 2 each time so its geometric. Plugging into the formula:

tn=3*[(2) ^(n-1)]

= (3)(2^n)(2^-1)

= [(3)(2^n)]/2

= (3/2)(2^n)