1. DAY 31: Agenda
Quiz minutes
Thurs

2. Unit 4: Sequences & Series
Accel Precalc
Unit 4: Sequences & Series
Lesson #2: Arithmetic Sequences and Partial Sums
EQ: What is the formula to find the sum of an arithmetic sequence?

3. What is the Explicit Formula for an Arithmetic Sequence?
Recall:
Find the nth term of an Arithmetic Sequence:
Arithmetic Sequence
--- ordered list of numbers with a common difference called d
What is the Explicit Formula for an Arithmetic Sequence?
Can find ANY term in sequence
an = _________________
*Open Form
an = _________________
*Closed Form

4. an = 4+3n – 3 an = 3n + 1 a13 = 4+3(13 – 1)= 40 a13 = 3(13) +1= 40
Ex 1. Write the explicit formula for the sequence 4, 7, 10, 13, …
*Open Form
an = 4+3n – 3
an = 3n + 1
*Closed Form
Then find a13.
a13 = 4+3(13 – 1)= 40
a13 = 3(13) +1= 40

5. What is the Recursive Formula for an Arithmetic Sequence?
Can only find the NEXT term in sequence
an = _________________
Ex 2. The eighth term of an arithmetic sequence is 75, and the twentieth term is 39. Find the first term and the common difference. Give the recursive formula for this sequence.
Common difference added to PREVIOUS term
a8 = 75 a20 = 39
an = a1 + d(n – 1)
75 = a1 - 3(8 – 1)
a1 = 96
d = -3
an = an , a1 = 96

6. Find the sum of a Finite Arithmetic Sequence
Generate Terms of an Arithmetic Sequence 2 Ways:
1st Way:
Repeated addition of d to the initial term

7. Repeated subtraction of d from the nth term 2nd way:
RECALL:
How can you solve systems of equations?
_________________________
________________________
Graphing
Substitution
We will use elimination to
derive the sum formula.
Elimination

8. Add these two versions of Sn.
a1 and an are both added “n” times

9. Ex 3. Find the sum of the odd integers 1 to 19.
The formula says we need to know n, the first term, and the nth term. 19
Since we are asked to find the sum of the first 10 terms, n = ______ 10

10. Ex. 4 Find S20 for the sequence
6(1) – 1 = 6 – 1 = 5
6(20) – 1 = 120 – 1 = 119

11. Finding the nth partial sum of an infinite arithmetic sequence--- sum of the first n terms of an infinite sequence
Ex 5. Find the 150th partial sum of the arithmetic sequence 5, 16, 27, 38, 49, …
1644

12. Find the sum of the rows:
Ex. 6 An auditorium has 20 rows of seats. There are 20 seats in the first row, 21 seats in the second row, 22 seats in the third row, and so on. How many tickets need to be sold to sell out this auditorium for an upcoming show?
To find the sum of all 20 rows, we need:
n = ____ d = ___ and a1 = _____ 20 1 20
What is the explicit formula for this problem?
Find the 20th term:
Find the sum of the rows:

13. ASSIGNMENT:
Textbook p odds #1 – 43,
59 – 71, 83 – 87
Thurs