M8L3 ~ M3 review

2. A SEQUENCE is just
an ordered list of
numbers.
Ex) an = 3n-1  2, 5, 8, 11,...

3. 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.

4. Below is the explicit formula for arithmetic sequences:

5. 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.

6. Below is the explicit formula for geometric sequences:

7. 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.

8. To see examples with recursive form
click here.

13. 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.

14. Because
infinite
geometric
series
converge,
you can
find the
sum using: