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

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Presentation on theme: "Arithmetic Sequences and Series An Arithmetic Sequence is defined as a sequence in which there is a common difference between consecutive terms."— Presentation transcript:

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2 Arithmetic Sequences and Series

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

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

6 T h e c o m m o n d i f f e r e n c e i s a l w a y s t h e d i f f e r e n c e b e t w e e n a n y t e r m a n d t h e t e r m t h a t p r o c e e d s t h a t t e r m. C o m m o n D i f f e r e n c e = 5

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

8 Formula for the nth term of an ARITHMETIC sequence. I f w e k n o w a n y t h r e e o f t h e s e w e o u g h t t o b e a b l e t o f i n d t h e f o u r t h.

9 Given: Find: IDENTIFYSOLVE

10 Given: Find: What term number is -169? IDENTIFYSOLVE

11 Given: IDENTIFYSOLVE Find: Whats the real question?The Difference

12 Given: IDENTIFYSOLVE Find:

13 A r i t h m e t i c S e r i e s

14 W r i t e t h e f i r s t t h r e e t e r m s a n d t h e l a s t t w o t e r m s o f t h e f o l l o w i n g a r i t h m e t i c s e r i e s. W h a t i s t h e s u m o f t h i s s e r i e s ?

15 71 + (-27) Each sum is the same. 50 Terms

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17 Find the sum of the terms of this arithmetic series.

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

19 Alternate formula for the sum of an Arithmetic Series.

20 Find the sum of this series It is not convenient to find the last term.

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