Warm Up Write the explicit and recursive formula

Warm Up Write the explicit and recursive formula 1. 3, 7, 11, 15…. 2. 6, 3, 1. 5, 0. 75… Find the 1 st 5 terms: 3. t 1= 4, tn= tn-1+5 4. tn=4(2)n-1 Find the 10 th term: 5. t 1= 3, tn= 3 tn-1 6. tn=2 + 4 n

Arithmetic Sequences and Series

Sequences List with commas 3, 8, 13, 18 Series “Indicated sum” 3 + 8 + 13 + 18

An Arithmetic Sequence is defined as a sequence in which there is a common difference between consecutive terms.

Which of the following sequences are arithmetic? Identify the common difference. YES NO NO YES

e c n e r e f f i d n The commo e h t s y a w l a is y n a n e e w t e b e c n e r e f f di t a h t m r e term and th. m r e t t a h t s proceed Comm on Differe nce = 5

The general form of an ARITHMETIC sequence. First Term: Second Term: Third Term: Fourth Term: Fifth Term: nth Term:

Formula for the nth term of an ARITHMETIC sequence. If we know three any o ough f these we t to b to fin e ab le d the fourt h.

Given: Find: IDENTIFY SOLVE

Given: Find: What term number is -169? IDENTIFY SOLVE

Given: What’s the real question? IDENTIFY Find: The Difference SOLVE

Given: IDENTIFY Find: SOLVE

Arithmetic Series

What is the sum of this series?

50 Terms 71 + (-27) Each sum is the same.

Find the sum of the terms of this arithmetic series.

Find the sum of the terms of this arithmetic series. What term is -5?

f o m u s e h t r o f a l u Alternate form. s e i r e S c i t e m h t i r A an

Find the sum of this series It is not con venient to fi nd the last term.

Vocabulary of Sequences (Universal)

Given an arithmetic sequence with x 38 15 NA -3 X = 80

-19 353 ? ? 63 x 6

Try this one: 1. 5 x 16 NA 0. 5

9 633 x NA 24 X = 27

-6 20 29 NA x

Find two arithmetic means between – 4 and 5 -4, ____, 5 -4 5 4 NA x The two arithmetic means are – 1 and 2, since – 4, -1, 2, 5 forms an arithmetic sequence

Find three arithmetic means between 1 and 4 1, ____, 4 1 4 5 NA x The three arithmetic means are 7/4, 10/4, and 13/4 since 1, 7/4, 10/4, 13/4, 4 forms an arithmetic sequence

Find n for the series in which 5 y x 440 3 Graph on positive window X = 16

The sum of the first n terms of an infinite sequence is called the nth partial sum.

Example 6. Find the 150 th partial sum of the arithmetic sequence, 5, 16, 27, 38, 49, …

Example 7. 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 seats are there in all 20 rows?

Example 8. A small business sells $10, 000 worth of sports memorabilia during its first year. The owner of the business has set a goal of increasing annual sales by $7500 each year for 19 years. Assuming that the goal is met, find the total sales during the first 20 years this business is in operation. So the total sales for the first 2 o years is $1, 625, 000