1. A sequence is ARITHMETIC if the differences between consecutive terms are the same.
ex. 2, 7, 12, 17, 22, 27
5 is the common difference.
an+1 = an + d
a1 is the first term
d is the common diff.
a1 = 2
an+1 = an + 5

2. ex. 3, 5/2, 2, 3/2, 1 Is this an arithmetic sequence?
Find the common difference (d).
a1 = ? an + 1 = ?

3. A sequence is GEOMETRIC if the ratios of consecutive terms are the same.
ex. 3, 6, 12, 24, 48, 96
2 is the common ratio.
an+1 = an  r
a1 is the first term
r is the common ratio
a1 = 3
an+1 = an  2

4. ex. 5, 1, 0.2, 0.04
Is this a geometric sequence?
Find the common ratio (r).
a1 = ? an + 1 = ?
Ex. a1 = d = 2 Write the first 4 terms of the sequence.

5. Ex. a1 = 7 d = 2 Write the first 4 terms of the sequence.
Ex. a1 = r = 4 Write the first 4 terms of the sequence.
Ex. a1 = ak + 1 = -¾ ak Write the first 4 terms of the sequence.

6. Finding the nth term of a sequence
Arithmetic: an = a1 + ( ) d
n – 1
n – 1
Geometric: an = a1  r
Ex. a1 = d = 4 Find a10
Ex. a1 = r = 3/2 Find a8

7. The sum of a finite arithmetic sequence with n terms:
 Carl Friedrich Gauss

8. The sum of a finite geometric sequence with n terms:
The sum of an infinite geometic sequence:
If |r| < 1
What happens if n becomes infinitely large?
What if |r| >1 ?