A SEQUENCE is just an ordered list of

numbers.

Ex)  an = 3n-1      2, 5, 8, 11,...

A sequence can be arithmetic, geometric, or neither.

2, 4, 6, 8, 10,… 2, 6, 18, 54,… 11, 101, 1001,… (add 2) (multiply by 3)

You need to be able to write & use the explicit formula and recursive formula for a sequence.

Below is the explicit formula for arithmetic sequences:

To find the common difference, subtract a term from the one before it.  

Ex) Given the sequence 4, 10, 16, 22,... let's find the common difference: 10 - 4 = 6    &   16 – 10 = 6  which means   d = 6 

If you need help finding the nth term or writing the explicit formula for an arithmetic sequence,

click to see a video example.

Below is the explicit formula for geometric sequences:

To find the common ratio, divide a term by the one before it.  

Ex) Given the sequence 4, 4/5, 4/25, 4/125, 4/625,... let's find the common ratio: 4/5 ÷ 4 = 1/5    &   4/25 ÷ 4/5 = 1/5    which means   r = 1/5  (or 0.2*)  *If your calc gives you a decimal, you can press MATH, ENTER, ENTER to

convert to a fraction (if it's possible).

If you need help finding the nth term or writing the explicit formula for a geometric sequence,

click to see a video example.

To see examples with recursive form click here.

Do you know how to tell if an INFINITE series converges(approaches a certain finite number)

or diverges (doesn't converge... could go to ∞)?  

Only infinite geometric series can converge, and only if |r|<1.

  Check out infinite series examples that either converge

or diverge by clicking here.

ALL FINITE SERIES CONVERGE as you’re only adding up a finite # of terms.

Because infinite

geometric series

converge, you can find the

sum using: