Download 4 – 6 Arithmetic Sequences WW: sequence, term, arithmetic

4 – 6 Arithmetic Sequences
WW: sequence, term, arithmetic sequence, common
difference
EQ: How is identifying an arithmetic sequence similar to
identifying a function rule?
When you list the times and distances in order, each list
forms a sequence. A sequence is a list of numbers that
often forms a pattern. Each number in a sequence is a
term. When the terms of a sequence differ by the same
nonzero number, the sequence is an arithmetic sequence.
The difference between the terms is called the common
difference.
Determine whether each sequence is arithmetic, find the
common difference if it is, and the next 3 terms
Ex1) 12, 8, 4, 0, …
-4 -4 -4
Arithmetic
CD: -4
Ex2) 1, 4, 9, 16, …
+3 +5 +7
Not arithmetic
Next three: -4, -8, -12
You try
1)-¾, -¼, ¼, ¾, …
2)2/3, 1/3, -1/3, -2/3, …
3)-4, -2, 1, 5, …
4)4, 1, -2, -5, …
Arith; CD: 1/2; 5/4, 7/4, 9/4
Not Arith
Not Arith
Arith; CD: -3; -8, -11, -14
Find the indicated term of the arithmetic sequence
Ex3) 22nd term: 5, 2, -1, -4, …
Step 1: Find the common difference: -3
Step 2: Write a rule to find the 22nd term
an = a1 + (n – 1)d
n = term number wanted
a22= 5 + (22 – 1)(-3)
a1 = the first term
a22= 5 + (21)(-3)
d = common difference
a22= 5 + (-63)
a22= -58
YT: 60th term: 11, 5, -1, -7, …
YT: 15th term: a1 = 7; d = 3
a60 = 11 + (60 – 1)(-6)
a15 = 7 + (15 – 1)(3)
a60 = 11 + (59)(-6)
a15 = 7 + (14)(3)
a60 = 11 + (-354)
a15 = 7 + (42)
a60 = -343
a15 = 49
The odometer on a car reads 60,473. Every day the car is
driven 54 miles. What is the odometer reading 20 days
later?
Step 1: Find d, a1, and n.
d = 54,
a1 = 60,473,
n = 21
a21 = 60,473 + (21 – 1)(54)
a21 = 60,473 + (20)(54)
a21 = 60,473 + (1080)
a21 = 61,553 miles
YT: Each time a truck stops, it drops off 250 pounds of
cargo. It started with a load of 2000 pounds. How much
does the load weigh after the fifth stop?
d = -250,
a1 = 2000,
n=6
a5 = 2000 + (6 – 1)(-250)
a5 = 2000 + 5(-250)
a5 = 2000 + (-1250)
a5 = 750 lbs
Answer EQ: You must find the difference from one number
to the next and turn it into an equation.