Chapter 13-Sequence

So Brob is back and this week she taught us all about Sequences!

-A Sequence is a list of numnbers
-Arithmetic sequence: a sequences that is generated by adding the SAME number each time.
Formula: tn = t1 + (n-1)d
t1 = 1st term
n = number of terms
d = diffrence (what is being added)
tn = term
-Geometric sequence are generated by multiplying the SAME number each time (to divide we use fractions)
Formula: tn = t1 x r^(n-1)
t1 = 1st term
r = what is being multiplied
n = term number
tn = __ term

Example 1: Is the following sequence arithmitic or geometric? Find the formula for the nth term.
3,5,7,...

This would be arithmitic because we are adding 2. Therefore d = 2. To find the formula for the nth term we need to plug numbers into the formula:
tn = t1 + (n-1)d
tn = 3 + (n-1)2
tn = 3 + 2n - 2
tn = 2n + 1

Example 2: Is the following sequence arithmitic or geometric? Find the formula for the nth term.
4,8,16,32,..

This is geometric because you multiplying 2. To find the formula for the nth term you need to plug in the numbers to the formula:
tn = t1 x r^(n-1)
tn = 4 x 2^(n-1)
tn = 4 x 2n x 2(-10
tn = 4 x 2n/2 : the 2 and the 4 cancell out
tn = 2 x 2n

Example 3: Find the first 4 terms and state if it is arithmitic or geometric
tn = 5n + 2

n = 1: 5(1) + 2 = 7
n = 2: 5(2) + 2 = 12
n = 3: 5(3) + 2 = 17
n = 4: 5(4) + 2 = 22
This is arithmitic

Example 4: Find the first 4 terms and state if it is arithmitic or geometric
tn = 3^(2n-1)

n = 1: 3^(2(1) +1) = 3^3 = 27
n = 2: 3^(2(2)+1) = 3^5 = 243
n = 3: 3^(2(3)+1) = 3^7 = 2,187
n =4: 3^(2(4)+1) = 3^9 = 19,683
This is geometric

--Danielleee