write the next term in the series. then write the series with summation notation. n=1 5 n 3n
TRANSCRIPT
Write the next term in the series. Then write the series with summation notation.
1 2 3 4
2 5 8 11
5
14
n=1
5
n
3n -1
Objective: (1) Using and Writing Sequences (2) Using Series
Agenda: 4/02/15Agenda: 4/02/15
1.) Warm-up
2.) Questions:
WS 11.1 Practice A #’s 1-27 ODD (Skip 11&13)
WS 11.1 Practice B #’s 1-25 ODD (Skip 11)
3.) Lesson: 11.2 Arithmetic Sequences and Series
4.) Class/Homework
5.) Work in Pairs/Groups
STAY ON TASK!!
11.2 Arithmetic Sequences and 11.2 Arithmetic Sequences and Series (Day 1)Series (Day 1)
In an Arithmetic Sequence, the difference between consecutive terms is constant.
The constant difference is called the common difference and is denoted by d.
Ex. 1Ex. 1 Decide whether the sequence is arithmetic. Explain why or Decide whether the sequence is arithmetic. Explain why or why not.why not.
- 3, 1, 5, 9, 13, …- 3, 1, 5, 9, 13, …
To decide whether a sequence is arithmetic, find the differences of To decide whether a sequence is arithmetic, find the differences of consecutive terms.consecutive terms.
d = 1 – (- 3) = d = 1 – (- 3) = 44 d = 5 – 1 = d = 5 – 1 = 44 d = 9 – 5 = d = 9 – 5 = 44 d = 13 – 9 = d = 13 – 9 = 44
Each difference is Each difference is 44, so the sequence is arithmetic., so the sequence is arithmetic.
11.2 Arithmetic Sequences and 11.2 Arithmetic Sequences and Series (Day 1)Series (Day 1)
6150 nan
dnaan 11
nan 656
RULE FOR AN ARITHMETIC SEQUENCE
The nth termnth term of an arithmetic sequence with first term a1 and common difference d is given by:
an = a1 + (n – 1)d
Ex. 2 Write a rule for the nth term of the arithmetic sequence. Then find a25.
50, 44, 38, 32, …
a1 = 50 and d = 44 – 50 = - 6, so the sequence is arithmetic. A rule for the nth term is: 2565625 a
1505625 a
9425 a
Memorize!!Memorize!!
11.2 Arithmetic Sequences and 11.2 Arithmetic Sequences and Series (Day 1)Series (Day 1)
Ex. 3 Write a rule for the nth term of the arithmetic sequence.
d = 4, a14 = 46
In order to write the nth term the “d” and the “a1” ARE NEEDED. To find a1 use the a14 and the following rule.
an = a1 + (n – 1)d
a14 = a1 + (14 – 1)(4)
46 = a1 + 52
- 6 = a1
an = - 6 + (n – 1)(4)
an = - 6 + 4n – 4
an = 4n – 10
Memorize!!Memorize!!
11.2 Arithmetic Sequences and 11.2 Arithmetic Sequences and Series (Day 1)Series (Day 1)
daa 115115 daa 1515
da 417 1
Ex. 4 Write a rule for the nth term of the arithmetic sequence.a5 = 17, a15 = 77
In order to find the nth term WE NEED to find the a1 and the d.We use the a5 and the a15 terms in the nth term for an arithmetic sequence.
an = a1 + (n – 1)d
da 1477 1
Memorize!!Memorize!!
11.2 Arithmetic Sequences and 11.2 Arithmetic Sequences and Series (Day 1)Series (Day 1)
da 417 1 da 1477 1
da 417 1 da 1477 1
d1060
d6
6417 1 a
2417 1 a
17 a
617 nan
667 nan
136 nan
HOMEWORKHOMEWORK
Page 663Page 663 15 - 37 ALL15 - 37 ALL
This is FUN!!!!!