13-1

We began Chapter 13 this week in Advanced Math. I3-1 is about arithmetic and geometric sequences. This section’s objective was to identify an arithmetic or geometric sequence and find a formula for its nth term.

Arithmetic Sequences - a sequence where the same number is added each time.
(Formula: tn = t1 + (n-1) d) The following sequences are all arithmetic..
Ex: 2, 6, 10, 14, 18.. – difference = 4

Geometric Sequences – a sequence where the same number is multiplied each time.
(Formula: tn = t1 x r^n-1)The following sequences are all geometric..
Ex: 1, 3, 9, 27, 81.. – ratio = 3

EX 1: 2, 5, 7, 10, 12.. Is it arithmetic, geometric, or neither?
A). It would be neither since you are adding 2 and 3 at different times. It isn’t a constant number being added or multiplied.

EX 2: How many multiples of 6 are there between 24and 300?
A). First find the multiples – 24, 36, 42, 48, 56.. 300
B). Since you are adding 6 each time, your difference = 4.
C). Plug the numbers into the arithmetic formula – tn = t1 + (n-1) d
D). 300 = 24 + (n-1)6
E). Solve using order of operations.
F). Your answer is n=47

EX3: Find t9 if t1=3, t2=6 and the sequence is geometric.
A). Since the problem is telling us it’s geometric, use that formula - tn = t1 x r^n-1
B). t9 = 3 x 2^9-1
C). t9 = 768